Welcome to a documentary which seeks to expose the sexual violation of animals who are used as breeding slaves for the meat, dairy and egg industries. Many of you may think that the dairy industry is the only industry to commit rape and violation of animals, but it is actually a fundamental part of all industries which produce animal products.  So today let's begin with one of the most obvious and well-known industries built off of sexual abuse and animal slavery, the shameful dairy industry. In the dairy industry, stud bulls are used for their semen. Semen collection generally begins at around 11 to 12 months old. A male teaser animal is at times used for mounting and the handler uses an artificial vagina for semen collection.  According to Farmers Weekly magazine, the stud bulls have access to a sand arena and playpen for exercise to keep them fit and healthy. Ah, so you give them a sand pen and some straw in exchange for sexual acts? That's not disturbing at all. In artificial insemination centres, bulls are typically collected two or three times per week, with two or three ejaculates per collection day. Bull handlers do not get involved in routine health treatments, so bulls only associate them with pleasurable activities. In some cases, stockmen have allocated bulls so they can build up a relationship based on mutual respect and trust. Okay, sounds like literal bestiality. Mutual respect? Doesn't mutual imply both parties are consenting? Animals are not capable of giving consent just like children.  And what happens to the stud bulls when you're done molesting them? They get retired to the local slaughterhouse and get turned into steak? This is painting a very disturbing picture already. Another disturbing way to retrieve semen from stud bulls is through electro-ejaculation. We've examined the bull, everything, so we're ready to do the collection. So Dr. Karpner is going to place the probe in the rectum for us. And according to veterinary sites, electro-ejaculation is now the safest and standard method of semen collection used by trained veterinary surgeons in the UK. The process goes as follows. A large probe is inserted into the rectum of the restrained animal as it delivers a current of electricity into the nerves of his anus until he ejaculates into the hand of a vet or farmer who is holding a vial for collection. This is usually collected using the electro-ejaculator. He's placed some lubricant on the probe. Now I'm going to go ahead and turn on the ejaculator and you will probably see the bull react. You can pull that pipe up one if you want to. Hopefully we will get an erection. You can see that he's reacting more so and he is putting out quite a lot of prostate fluid.  Always make sure we examine that penis. Now the bull is starting to ejaculate somewhat. Here you can see some of the clear fluid coming out during the collection and we'll keep repeating this process five to ten times in order to get a nice collection from this bull. So there we have it, we've got our bull collected now. There was no pain associated with it, no anguish, very minimal stress. Okay, so you're straining the animal in a cattle crush and raping with an electric dildo until he ejaculates. Sounds like these farmers have a very distorted sense of what caring for animals actually means. This is just sodomy and molestation. Imagine what's going through their minds as they're being restrained and penetrated. These animals are vulnerable like children and must be left feeling violated and confused. In order for cows to produce milk they have to be pregnant or have recently given birth. Dairy farmers like to control this process themselves. Cows will show they're on heat by standing to be mounted and may have some mucus on the towel around their vulva. Farmers might use paint or chalk to see if the cows have tried to mount each other. You're looking for differences in the chalk or chalk that may have been rubbed off to indicate that the cow may be in heat. After determining which cows are on heat the farmer or vet will restrain the animal in a cattle crush. It's not comfortable for the cow to have an arm shoved into her near shoulder deep so they have to be held down for safety reasons apparently. One of the most disturbing parts of this whole process is the cows age. We're talking about very young, vulnerable animals. How confused and scared they must be. With the help again of the popular farmers weekly magazine here's a step-by-step process for the legally sanctioned sexual abuse of cows. On the farm our first choice for breeding our cows is artificial insemination which is the veterinary procedure of placing semen into the uterus. First stick on a full length arm glove and lubricate it. The farmer or vet will prepare the cow by wiping clean her vulva with a paper towel. Now they'll form a cone with their fingers and insert their arm into the rectum of the cow while keeping the towel aside. Of course not forgetting to work out any excess poop. You can see there's manure inside the rectum. So the first thing I'll do is clean out that manure and then try to clear out any air or anything. From here I can clean out any manure that's in the rectum. Now they'll locate the cervix of the cow through the wall of the anus and use downward elbow pressure to part the lids of the vulva and guide in the AI gun until there's a release of resistance. The semen will be deposited near the uterine horns where the cervix ends and the uterus begins. The end goal is to get your gun through the rings of the cervix into the uterus and then deposit the semen right there. Then right away get the semen into the cow so that it stays warm. And that's how farmers rape animals so they can steal their milk and children. The process is repeated and repeated until the animals are no longer of economic use to the farmer and they'll be sent off to be murdered for their flesh. Now I know how uncomfortable it is to hear this process being explained to you. It's even uncomfortable for me to be explaining this. But just for a moment in your feeling of discomfort just imagine what it feels like to actually have this done to yourself. Put yourself in the animal's position. A young childlike conscious being oh that is super being restrained and violated.  I feel deeply embarrassed at the actions of our race. Stud bores used for semen collection or formating with females are often kept in cages similar to sale stools. Naturally pigs would usually select their mate and went to breed but these decisions are completely controlled and manipulated by human exploiters in the pork industry. The artificial insemination method is used by many pork producers. The bores are generally trained to mount a dummy partner for arousal. The bore mounts the stool. He's been trained before when he was younger. He's about 10 months old now and you can see now he's jumping the stool. The pig has the second longest orgasm of any animal and the camel has the longest orgasm. We're about to see the second longest orgasm in the process now. Then the collector will squeeze and massage the preppers or foreskin of the bore to expel the fluid that can accumulate there to collect the semen in the collection device. Bores actually have a small sack right here inside their prepues that can collect fluid and sometimes urine. This is the reason that vigorous massage on the prepues prior to semen collection is important to clean out all of that fluid. Wow, jacking off pigs in the pork industry is common practice? Who would have thought? The semen is then stored in preparation for AI in breeding sales. The UK has been known to export large amounts of frozen pig semen to places like China. As a result of the significant increase in semen demand places like Derpac Pedigree Pigs is now undergoing expansion. Again, I asked the question, what happens to the stud bores when their semen production declines? Did they get a visit to the local gas chamber or a date with the electric stunning clamps and a butcher's knife in the throat? Let's move on to the process for the female pigs, the sows. Breeding sows generally go into heat at the very young age of 6 to 8 months old. After heat detection, which some farmers have a more hands-on approach to determining, the AI process will begin. The backyard method of AI involves sitting on the backside of the sow to mimic the mating process and inserting a catheter which mirrors the shape of a boar's penis. Let's not use euphemisms here. It's essentially a pig's dildo filled with a jaculate. During PCAI, a foam tip or spiral-tipped outer catheter is inserted into the vulva through the vagina and placed in the first two interdigitating pads of the cervix.  It's also very disturbing to see a family getting a small child involved in this process, which really shows how early animal abusers are indoctrinated and taught to exploit animals. Locks into the cervix. They squeeze the tube. A more commercial operation might employ the use of a raised catheter referred to as a pork store or an AI saddle, which is a very bizarre instrument indeed. Here's some footage from Australia which shows the worker trying to mimic the boar by sitting on the pigs behind and also using a boar to stimulate the breeding sows. After impregnation, sows will be sent to either a gestation crate, sow stall or group housing, depending on the country's guidelines. This is where the sows will spend their pregnancy before being moved to the horrific sparring sheds after having their litter. As you can see, these animals stand no chance against their human oppressors and are being violated and raped so that consumers can enjoy a morsel of their flesh. How is this sexual abuse and predation allowed and sanctioned by the government? How do you feel knowing that when you pay for animal products, you are funding animal abusers to molest animals? Sheep are most commonly exploited for their flesh in their wool. In terms of sexual exploitation, sheep have proved to be a little more difficult to find information on, which is raising suspicion. From the research we have conducted, AI is not the most common form of impregnation for sheep. However, in recent years, it's clearly becoming more widely advocated to farmers. According to Farmers Weekly, increasing numbers of sheep producers are following in the footsteps of their dairy counterparts by using artificial insemination as a means of improving genetic traits in their flocks. Generally, ram masturbation and semen collection will carry out as follows. A teaser you will be restrained in a headstool. A ram is then let in to the collecting area.  We fill it up with hot water so it keeps it at the right temperature. We have these. We put that in there. And this is just to keep it all warm as well. And that is what we use. Very simple and very effective. The ram then mounts the you.  The prep use should not be grabbed or yanked towards the AV but rather gently guided in. A final upwards pelvic thrust signifies ejaculation. Donna will take around five collections of semen from the Rams each day. A task that can prove to be somewhat challenging. The semen will then be stored for the disturbing artificial insemination process. Looks like the semen collector was having quite a good time considering how inappropriate and bizarre this whole process is. If that wasn't weird enough the insemination process for the female sheep is even weirder. There are multiple ways for sheep to be artificially inseminated including vaginal, cervical and laparoscopic. Laparoscopic AI is typically favoured in the UK because semen is deposited directly into the uterus making conception rates higher and frozen semen can be used. In the laparoscopic method the A2 is restrained upside down in a terrifying, medieval-like contraption called an AI cradle. Right, so the oil here is just clipped and surgically prepared and we make a small incision on the left and small incision on the right and there's a 10mm control here that's what we use to make the incision on the left-hand side that's the side that the scope can go through. She is then cut into on the left and right hand side above her udder. In the goat's blunt it goes in. A camera is then inserted to view the womb. The sheep appears to be conscious and is moving around in an uncomfortable way as the man pumps gas to displace the stomach and intestines. The semen is then probed and prodded into the right-hand side of the U. AI is becoming increasingly advocated over the old-school way of breeding because a ram with good quality semen, adequate testicular size and a good libido can breed up to 100 U's in a season whereas artificial insemination can magnify the breeding potential and genetic influence of a single ram by many times. One ram could be used over several hundred U's rather than possibly that one ram being used over just 50 U's so we're able to spread those elite ram's genetics across a lot more U's and have a greater genetic influence. What is seemingly a more common practice for breeding sheep involves the following. The U's have their reproductive organs exploited through the controlling of their cycle and sponging. Sponging synchronizes the U's so they all come into mating season at the same time. And then this is the little applicator. Like you're using the same applicator on all the U's so this kind of cleans it but it's a lubricant too. So I just do that and then it's all lubed up. Insertion should be easier.  Two weeks later the sponges are removed and the sheep are injected with PMSG to increase ovulation. Brain relapse will be administered in PMSG. The ram is then introduced to the herd to have his way with the young female sheep. Sheep are branded with paint to show that they have been successfully mounted by the ram. When these sheep are no longer a profit to the farmer they are all of course sent to be brutally executed and decapitated in a slaughterhouse. All I see here is human domination, manipulation, exploitation and violation of vulnerable and defenseless animals so they can be murdered for monetary gain. All you need to do to really see how disturbing and unjustified this behaviour is is to put yourself in the animal's position. Let's start with broiler chickens. Broiler chickens are specifically raised to be murdered for their flesh. Broiler chicks come from their parent breeders who are kept in specific sheds for breeding. Parent birds are raised and kept until approximately 64 weeks and produce about 160 fertile eggs. These eggs will hatch and produce the meat chicken flots whose flesh is processed for human consumption. The most common practice for breeding parent birds is the introduction of roosters to the barn. There is typically one male to every 10 breeder hens placed in the laying barn. Roosters are known to be aggressive around other males and towards hens when mating. So to introduce so many of them to overcrowded confined sheds can only be described as cruel as the birds have no way of escaping each other. One of the most harrowing accounts I've ever seen from inside a parent breeding shed is from animal liberation activist Patty Marks. Many of the hens of this shed are red raw. There's no feathers on their backs at all.  What Patty described is called spiking a flock. Older males are removed and slaughtered and younger males are introduced to a more sexually active. The breeding hens really don't get a break and are repeatedly mated. A less common but still practice method for breeding farm birds is AI. And for this practice most farm birds undergo a similar process. First let's explore the process for seaming collection from the rooster. The rooster is pinned down unable to move in its massage to stimulate the copulatory organ or the phallus. This is followed quickly by pushing a towel forward with one hand and at the same time using the thumb and forefinger to apply pressure to the area where the semen is then milked.  Just about the right size for sucking up any of the sperm that you get.  This here is just blatant bestiality. This poor rooster has been sexually molested to have his sperm stolen. I wonder if this woman finds it weird or perverse to be holding down a defenseless being and sexually arousing him. Now onto the hen. Again, here the hen is restrained. Her cloaca is exposed and a pipette with semen is inserted into her vagina. Can you imagine what this would be like held down against your will and forcefully penetrated? How confused and terrified these birds must be. Parent birds are systematically exploited for their reproductive systems and have their eggs taken away and placed in an incubator which is an artificial way of hatching. When broiler chicks are just a day old they're transported in modules called chick boxes from the hatchery to the rearing farm. The chicks are placed in the rearing sheds and kept in large mixed sex flocks. 10,000 to 20,000 birds or many more are kept in a single shed. The chicks are slaughtered at an extremely young age at around 6 to 7 weeks old. These are just little babies in overgrown bodies. In the meantime parent breeders spend their life going through a distressing cycle of reproduction. Kept in laying sheds being mated where they rarely see the light of day and then at the end of it all are murdered to be eaten by the unaware consumer. Egg laying hens follow a similar distressing life of reproductive slavery. Chicken breeds specific to egg laying are born in a hatchery. The males are deemed useless and do not produce eggs so they are destroyed via maceration or gassing and the females are moved to a rearing site.  At around 60 to 70 weeks of age egg production will slow down and the hens will be sent to the slaughterhouse. Artificial insemination of turkeys is similar to that of chickens but is standard practice worldwide. Turkeys have been selectively bred to grow twice their natural size and are now too heavy and overgrown to naturally mate. So must now be artificially reproduced.  In this semen collection class you can see that the turkey is forcefully pinned down and masturbated.  The female turkey is restrained and the semen is forced into her. As you can see she is shaking and so terrified that she shits herself. How can we think that this is acceptable to put animals through this vile perverted process to impregnate them against their will and without their consent? Now all the guys are doing my artificial insemination. They do between five and six hundred birds an hour. Each bird gets artificial insemination once a week. We have four barns so we do this four times a week. Recently technologies have been introduced to make female penetration more efficient for large skull insemination. This involves an insemination bench where the turkey is clamped down and molested. We could find turkey AI footage from nearly all over the world but wait what about the UK? With around 14 million turkeys slaughtered in the UK for meat in 2017 alone and at being standard practice to artificially inseminate turkeys in the UK? Where's all the UK footage? What's the matter UK turkey farmers? Are you too afraid to show us how you fiddle around with turkey's private parts for profit? Where's all the UK evidence of high welfare turkey molestation? That's right, not even the fish are safe from humans in their lust to dominate, control and commodify through the exploitation of the reproductive organs of every animal on earth. According to the UN Food and Agricultural Organization 2018 Fishery and Aquaculture stats, the contribution of farm fish to total fish use has risen over the years reaching 46.8% in 2016 up from 25.7% in 2000. This figure amounts to about 80 million tonnes of farmed food fish annually compared to about 90 million tonnes of wild captured fish. Farm fish have recently superseded wild capture fisheries as the main source of seafood for human consumption. While almost all farm fish production is destined for human consumption, the proportion from wild capture fisheries now stands at around 78%. Salmon consumption worldwide is three times higher than it was in 1980. Salmon aquaculture is the fastest growing food production system in the world, accounting for 70%. That's 2.5 million metric tonnes of the market. It is scientific consensus that fish are sentient beings who feel pain and suffer. So please understand that this process, although may not look like it to you as we all express pain differently, I can assure you these fish are suffering. Salmon are removed from the water where they'll immediately begin to suffocate and are thrust onto a conveyor belt into a factory-like setting. These animals are sorted and the female is stung via an automated percussive system, which is the predominant method used for stunning commercially, whereby an air-powered hammer-shaped cylinder delivers a forceful blow to the head of each female salmon. Female is then sacrificed in a brutal fashion. Her stomach is sliced open and her eggs are removed. When they're ready to spawn, we'll kill that fish, which sounds really rough. Male salmon who are ready for spawn are then milked or essentially masturbated into the container of salmon roe, which is then mixed ready for incubating. Catfish is the leading aquaculture-produced seafood product in the US. The annual harvest of farm-raised catfish in the US is at least twice as much as the annual aquaculture production of all other species of fish and shellfish combined. Annual production over the last decade has ranged from about 500 to 650 million pounds. The stripping of female catfish is a procedure where the animal is taken out of the water and dried with a towel with the cloaca exposed. A finger is then run down the underbelly to push eggs out of her into a bucket. The male spawner has to be sacrificed an hour prior to the stripping of the female eggs to obtain the milk, which in catfish cannot be gotten through the same stripping process. The procedure on the male fish is carried out by cutting open the abdominal area to expose the testes for easy dissection. The milk, or fish semen, is then extracted and mixed in with the eggs to fertilize them ready for incubation. Now that was absolutely awful. Global farmed shrimp production in 2016 was more than 5.7 million tons. The top importers of shrimp, both farmed and wild caught, are the European Union and the United States. Now one of the weirdest things I've ever seen since I've been looking into the ways humans sexually exploit animals is seeing a shrimp being jacked off by a human. Although it's uncertain at how common this practice actually is, the fact that it's even practiced at all was just weird. Apparently the procedure for artificial insemination in shrimp goes as follows. A female shrimp with mature eggs or ovaries is selected. The male shrimp is essentially jacked off to extract the sperm mass from the sperm metaphor and the prawn semen is then inserted into the female. Now come on, this is just getting out of control. The last animal or more like insect I'd like to feature is the small but significant honeybee. And I'll let my friend Sonia say explain this part. Hi everyone, bees will only produce honey if they have a queen. Queen bees are often artificially inseminated, which means that the honey industry first kills by crushing and squeezing a male bee to take out his semen and then they forcibly inserted in the queen bees vagina. Wow, is there an animal on earth we haven't sexually exploited for our own gain? I don't know how many actual parents are watching, but I damn sure know that almost everyone had a parent of their own at some stage of their life. So it really shouldn't be hard for you to empathize with the trauma that these animals have to go through when their families are torn apart. Dairy cows experience serial rape and kidnap through their five to eight years of milk production. The calves will generally take the first drink of the udder called the colostrum and after this they are separated from their mother to ensure no further milk is taken so that profits are maximized. Here she is behind me here, she just lost her child, that's probably one of the saddest things I had to witness, that poor innocent little calf. The kidnapping of calves happens across the board in all commercial and backyard dairy farms. It is arguably one of the cruelest things you could do to a mother. The only time you'll ever see these gentle animals show anything close to aggression is when they're having their calves taken from them. Not sure what it is about this pasture this year, but these cows have not wanted us around when they've been tagging these calves. It's a pretty little calf, a little calf that's trying to get out. Here's just a little heifer.  I just want to tag your baby! I just want to tag your baby! The mothers can be heard pining for their young for up to five days after their baby has been taken and in some cases the calves are left in hutches not too far from their mothers. Just across the road here, not even 10 meters away are the mother cows. How horrific to be separated so close to so they can hear each other.  The psychological trauma these animals go through can only be imagined. Mothers have been known to put up a fire for the first two or three times their calves are taken but after that they may lose hope and stop fighting. Male calves are either shot in the head on their first day of birth or raised for veal or beef where they'll be executed and dismembered in a hell-hole murder factory. Look at this.  Adducted female calves will suffer the same fate as their mother.  After giving birth to their litter, pregnant sows are kept in farrowing crates where they cannot turn around. The mothers are kept here for up to five weeks while their piglets are suckling. I've been in farrowing sheds and I can tell you from experience.   She looks exhausted. Absolutely exhausted. Pigs are known to suffer deep psychological trauma from being in confined spaces. Pigs are usually clean animals but are forced to live in their own waste. Crushed and dead piglets in the crate with the mother are not uncommon. So right next to her face in the feed tray is one of her dead piglets. How horrible and she cannot even get up or try to help or do anything. It's almost better to have died young than to have lived a life like this. Once weaned, the piglets will be taken to weaner sheds to be fattened up for the pig flesh industry and will generally be murdered at about five to six months old. Pigs would naturally live to about 15 years but breeding sows in the pork industry barely make it past three years. They suffer a constant cycle of forcible impregnation, gestation, horrifying farrowing crates and the despair of experiencing the serial abduction of their young. When sows are spent and no longer economically viable, these exploited mothers will go to a gas chamber where they will suffer and die and their bodies will be used for second-hand cuts of meat for foods like sausage rolls. This is how the meat industry treats mothers. After around a four to five month pregnancy, a U gives birth. The lambs are generally removed from their mother at around two to four months old.  So it could be argued that the connection with their young has had more time to form and the suffering from the loss is magnified. Lambs under natural conditions nurse for at least six months. The abducted lambs will either go on to be breeding sheep or they'll be reared for their flesh.  In the UK as many as 15% of lambs do not survive. After spring lambing, the U mothers will then only have a few months before autumn topping when the process starts all over again. So again, an endless cycle of emotional suffering and kidnap of their children until the breeding mothers face the same fate as every other animal exploited in the meat industry. They'll be murdered for their bodies. Broiler chickens are raised specifically for their flesh.  In natural circumstances, the mother hen would help the chicken hatching and raise her chicks from there on. The heartbreaking reality is that the mother will never have a chance to meet her chicks and instead follows a continuous cycle of distress. Her reproductive system is exploited over and over until she's no longer profitable and she too is murdered for her flesh. Egg laying hen parent breeders will in the same way never see their eggs hatch. They will be repeatedly mated by introduced roosters, have their reproduction system continuously exploited until they are completely exhausted, their egg production declines and they too will have their throats slashed open in the slaughterhouse. Upon hatching, chicks in the egg industry will be separated based on sex. Studies show that chicks are able to recognise their siblings upon hatching. So to be separated at birth is a distressing reality for newborns. But the male chicks distress will be short-lived as immediately after sorting they are dropped fully conscious into a macerator where they are blended up alive. The females will become egg laying slaves until their production declines and they too will be executed just like their parents and their exhausted, suffered bodies will be eaten by human beings. Oh my god, so good. So as you can see, sexual or reproductive abuse is not the only integral part of animal agriculture. The separation of murder of families is standard and necessary for commercial farmers to maximise their profits. Again, I ask you to please put yourself in the animal's position. Try to feel what it would be like to have your family torn apart. Ask yourself, is that cheese worth the life of misery? Is that bacon sandwich worth a mother's pain and anguish? Are those eggs worth a life of slavery and a certain brutal death for an animal you may never meet? Please understand that these industries only exist because of you, the consumer, and the power is in your hands to stop this. What is insane to me is that although these practices seem to be legally sanctioned we can also find laws across the western world which strictly prohibit sexual acts with an animal, aka bestiality.  Bestiality laws in the UK are as follows. Whosoever shall be convicted of the abominable crime of buggery committed either with mankind or with an animal shall be liable at the discretion of the court to be kept in penal servitude for life or for any term not less than 10 years. Looks like all those who tamper with animals in animal ag could be looking at a life sentence in the UK. Buggery is defined as anal intercourse. Is this not what the UK dairy industry does to non-consenting male and female animals when they probe restrained bulls for semen collection and use a fist to penetrate the rectum of female cows for insemination? It seems we've found a clear contradiction here. According to Animal Legal and Historical Centre College of Law there are only four US states who do not have laws prohibiting the sexual assault of animals. So that leaves 46 states where animal agriculture is committing crimes against animals in the form of bestiality. Moving on to Australia, every state has laws prohibiting bestiality. In New South Wales you could be looking at 14 years for fiddling around with the privates of an innocent animal. Looks like Australian animal farmers might be at risk of legal action for their offences against young and vulnerable sentient beings. What baffles me is that we live in a society that defends children vehemently against sexual predators. We understand the vulnerable and innocent nature of children which is why we have hefty sentences and even street justice to combat sexual offenders. We also understand that children just like animals are not capable of giving consent for sexual acts. And let's not forget the trauma a young confused child might experience after falling victim to this type of abuse. So couldn't we too compare the trauma experienced by beings of a similar sentient capacity like those innocent animals in animal agriculture who are literally sexually molested every second of every single day worldwide for animal products? Here we see exposed by surge investigators a worker who works at a dairy farm linked to the deputy president of the National Farmers Union inappropriately interfering with the young cow's vagina. Watch as the young cow cowers towards him confused as the offender comforts the cow by patting her on the face. This disturbing act resulted in disciplinary action against the perpetrator.  But if it truly were artificial insemination, shouldn't a subject be consenting?  If they are non-consenting or, like a child, unable to consent, it's no longer artificial insemination. It's rape. Through the victim's eyes, from the animal's perspective, how are they to know the difference between a worker inappropriately touching them for sexual gratification or a farmer inappropriately touching them for artificial insemination? Through the animal's eyes, they are being violated either way. This is all sexual abuse, and it needs to end. I have a suggestion. Considering the laws protecting animals from bestiality, how about we file a lawsuit against every single one of the sexual predators who molest animals for monetary gain? Or what about those good-hearted people who pay, via supply and demand, for the same sexual abuse that society appears to morally condemn? How do you feel, as a consumer, paying for the rape, violation and sexual abuse of young animals? Is it not you who are putting the animal abuser in business? Animal agriculture does not exist as it stands without the systematic sexual abuse of animals. So, if you oppose these crimes against animals, then it is an obligation that you oppose animal agriculture via your consumptive choices. To be vegan is to oppose all animal abuse.


Hello and welcome back to this 11th lecture of Microsystems Fabrication by Advanced Manufacturing Processes. So, so far we were looking into the mechanical processes like abrasive jet machining, powder blasting, also USM ultrasonic machining and we did those processes from a fundamental standpoint and then also model very various important issues like material removal rate or surface average surface roughness etcetera and then also try to understand the direct applications of such processes in the micro systems business where micro devices are manufactured from these mechanical so called energy processes. Today, we will be looking into a slightly different aspect into the electrochemical machining that is another very important non-conventional machining process or fabrication process very widely used again in the micro systems fabrication and as the name suggests electrochemical has a component of electricity and is also related to the chemical aspect which means essentially it is a ion transport. So, as any other electrochemical process would be this machining also involves the transport the material removal getting removed by means of displacement through ions into an electrolyte solution you need conducting surfaces for such machining operations and then the idea is that instead of depositing on the tool side if supposing the ions that emanate out of the workpiece material they can be somehow precipitated into a state which is undissolvable. So, they can be like debris and by circulating the electrolyte you can carry away those materials away from the main work zone and that way you can do bulk micro machining by using electrochemical operations. So, let us look this process at this process from a fundamental standpoint as we always normally do. So, it is one of the again electrochemical machining is one of the most sort of wanted and unconventional processes that are existing. The process is a reverse of electroplating some minor modifications and again it is based on the principle of electrolysis that can be seen from the way that the process is described. So, as you already know that in a metal in a piece of metal electricity is typically conducted by free electrons but in the solution the electricity actually gets converted or the electricity gets carried by ions. So, in metal on one side the electrons are kind of bound within the clutches of the nucleus formulating sometimes part of a large cloud electron cloud which moves around the various orbitals. But in solution the major current comes out of the ions and the mobility of those ions in the solution. So, the flow of a current in an electrolyte always is accompanied by movement of matter as opposed to what typically would happen in metallic conductors where it is really the electron of the hole in vacancy which is moving around and that results in a current and somehow this movement of current on an external circuit should be somehow balanced to the movement of charge carriers or ions in the solution for creating a continuous process or continuous state of operation. And so electrochemical machining is to establish that kind of a continuous operation where charge carriers on the solutions are kind of neutralized by the electrons and holes carried from the in the external circuit of such a process. So, as you can see here back in the slide in the ECM process the workpiece is connected to the positive electrode. So, it is made the anode and the tool to the negative terminal for the metal removal ok. So, that is conventionally followed in some of these processes. So, tool is the cathode and the workpiece is the anode as you can see in this figure here and one good point that I would like to mention here is that it is a dye sinking process meaning thereby that whatever is the profile of the tool however complicated the profile of the tool may be is kind of impinged or impregnated into the workpiece surface eventually because of the improper distribution of the electric field to begin with ok. So, electric field as you all are aware is basically the gradient of potential and the distances as you can see between this and this is quite large ok. So, the sides here of the tool are at a much higher distance thereby meaning that the electric field here is lower ok and the electric field here is very very high as can also be illustrated by this field lines ok. You can see the density of the lines closer to the interface which is closer of the tool surface in comparison to the sides. So, therefore, it is obvious to assume that if by Faraday's principle we assume the material removal rate MRR to be proportional to the to the electric field somehow. The field vectors are very high at the center and sort of trace amounts at the sides which means thereby that the MRR from the central portion of the workpiece would be the highest ok. So, MRR is highest where the tool is closest ok and the MRR subsequently is lower as you move to the sides and therefore, it is obvious to assume that the workpiece would kind of achieve a shape after a while where the electron electric field kind of gets homogenized and beyond which the whole shape the in the negative of the shape of the the tool electrode is impregnated and the ECM process gets carried out after that in the same shape as once this full impregnation and shape of of the tool is embedded onto the workpiece surface. So, that is what the beauty of this ECM process is that it is a dye sinking process. So, whatever shape you want to generate you create a negative of that shape as a tool and it automatically impregnates that shape finally on the workpiece. So, this can be also sort of more mathematically represented by the Ohm's law. So, which is actually followed here v equal to IR potential is current into the resistance and here we just sort of modify this is rho d over a where d is the distance between the two electrodes and a is the interfacial area between the the two electrodes and so therefore, we can easily find out that v v by d which is nothing but the electric field the magnitude of the electric field is actually equal to rho times of the current density. So, this actually is the magnitude of the current density and so therefore, electric field is proportional to the current density meaning thereby that if current density is more the electric field would be higher and vice versa. So, the current density definitely is more here in comparison to here because you have more amount of current travelling for so, because of the increased electric field as can be seen here. So, you have more amount of current density at the center because the E field is high and less amount of current density at the sides because the E field or the electric field is lower and MRR of course, as I told you before is proportional to the current density. So, therefore, if E field is high meaning thereby the current density is high the MRR also is high and vice versa. So, that is how electrochemical machining is really performed and that is how you know the dye sinking nature of the ECM process comes. So, there are certain basic fundamentals about this ECM electrochemical machining process one of them is that the tool is provided with a constant feed motion and as I already mentioned before that the whole idea is to somehow be able to precipitate whatever comes out of the workpiece of the anode and that precipitate can be circulated outside the work zone by means of the electrolyte which is a flowing or a moving electrolyte and that way the debris removal would mean that machining would happen. So, the electrolyte has to be therefore, circulated. So, it is pumped at a high pressure through the tool and the small gap between the tool and the workpiece and the electrolyte so, chosen is such that the anode is dissolved but there is no deposition on the cathode meaning thereby that whatever properties the electrolyte has would let the anode iron out but also precipitate the ions released. So, a fundamental choice in any ECM system is to first be able to identify what electrolyte would do that with what pair with what paired electrode which would be the tool in turn. So, the order of current and voltage that are normally found in such processes are a few thousand amps current and about 8 to 20 volts voltage in the gap of the ECM where the ECM is conducted between the tool and the workpieces typically about 100 to 200 microns 0.1 to 0.2 millimetres. Typical material removal rates can be about 1600 millimetre cube per second for about 1 kilo amp current. So, this is how highly energy you know so, it is a high energy process typically energy densities are very very high specific energy of the material is very high and just some other factors figures approximately 3 kilowatt hour of power are needed to remove about 16,000 millimetre cube of metal and this is about 30 times the energy required in any conventional process. So, in general we what we are seeing with when we did this mechanical processes or even now in electrochemical processes is that these non-conventional advanced machining processes are very highly energy intensive. So, the question is why do you use them? So, the first reason the although the processes are low yield is that you can more accurately do surface finishing and also if you can somehow constrain the operations to a very small zone you can do micro machining very wonderfully. Particularly let us say for example, the modality involved in the ECM process would make it amenable to crevices or corners which may not be otherwise get machined or be able to get machined by a conventional process as such which involves a metal to metal cutting. So, if supposing the shape complexity of the final you know product that you want to make is huge some of these non-conventional processes are really better choices over the conventional processes even though the fact that the yield is low even though the fact that the energy density which is needed for removing a certain volume of metal may be very high energy required may be very high and energy density may be higher. So, still do people do use because of shape complexities because of surface finishes particularly in micro system designs sometimes very complex shapes need to be fabricated and there is no other choice left apart from some of these non-conventional ways and means of fabricating. So, that is the reason why non-conventional processes go hand in hand with manufacture of micro systems or micro machine systems so on so forth. So, let us look at some of the other aspects of ECM as we have already illustrated here the electrolyte has to be flowed somehow between the tool and the workpiece and the best way to do that is to sort of coaxially move the electrolyte as you can see here this electrolyte is being moved through this coaxial tube which is actually present at the center of the tool and there also needs to be provided some insulation at the sides of the tool to ensure that the machining is not done sideways the machining is only done in this vertical manner. And then of course this tool should have constant feed motion so there has to be a precise control on the feed motion of the tool and then of course the electrolyte which is splashed needs to be collected and circulated back into the pumping system so that the debris which moves along with it can also go and does not clog the gap the very small gap between the workpiece and the tool. So, with the ECM the advantages are that the rate of metal removal is independent of the workpiece hardness. So, the workpiece may be of any hard hardness value there is no scribing as such which is involved or there is no plowing action which is involved so it is not mechanical and therefore the dissolution is really a property which is electrically dependent and you need not have a higher force typically to remove the material which may happen in a conventional process. So, hardness does not matter here any kind of hardness can be machined aminably because the basic principle is dissolution because of ions coming out of the surface. So, it becomes advantageous when the either the work material pauses very low machinability or the shape machine to machine this complex. So, this I have emphasized greatly in the last slide and unlike most other conventional and unconventional processes here there is practically no tool wear although that is not true really because sometimes great pressures get generated into the small gap here which may be a reason for tool deformation even if not wear. But the idea is that because there is no deposition on the tool as such or there is no change in the characteristics of the tool as such whatever comes out of the work piece goes into the solution and gets precipitated and this precipitate is getting carried away. So, the tool should be left alone by enlarge by this process and the wear of the tool is miniscule actually. So, though it appears that since machining is done electrochemically the tool experience is no force the fact is that the tool and work are subjected to large forces and we will do some design problems later where we will try to find out whether these forces are in consonance with the ultimate flow stress sigma of the tool side which would give you a feasibility or non feasibility of the process in question. So, we will do some of these design examples when we discuss this in some more details later and electrochemical machining. So, let us now look at a little bit of modeling about how you know material removal in such a ECM process electrochemical machining process can be predicted. So, the basic theory theories which come to our mind or the basic formulations which come to our mind are the Faraday's laws of electrolysis. So, let us see what those two laws are. So, fundamentally which govern this whole machining process as this is as good as any other electrochemical business. So, the Faraday's laws are pretty much valid in the machining process also. So, one the first Faraday's law says that the amount of chemical change produced by an electric current that is the amount of any material dissolved or deposited. So, that is essentially what the current is going to do either carry out ions or deposit ions to the electrodes that is proportional to the quantity of electricity that is passed. So, if current is higher current that is passed is higher the amount of chemical change produced by the electric current will also be higher which typically means the material dissolved or the material deposited would also be higher. So, that is the first law on the second Faraday's principle or law of electrolysis says that the amount of amounts of different substances dissolved or deposited by the same quantity of electricity are proportional to their chemical equivalent weights and this chemical equivalent weight as we will just see little bit later is basically the is a function of the total atomic weight and also the function of the valency state in which it has to be moved. So, if it is moving by plus 2 the chemical equivalent weight would be the atomic weight by 2 so on so forth. So, it is a function of the valency at which the ion is coming out and also a function of the atomic weight. So, the amount of different substances dissolved or deposited by the same quantity of electricity are proportional to their chemical equivalent weights. So, in quantitative form the Faraday's two laws can be stated here that the mass weight in grams of a material dissolved or deposited is proportional to the current in amperes. So, i is from here at the time for which this current flows time in seconds and this gram equivalent epsilon weight of the material which is actually equal to the atomic weight per unit the valency of the material. So, atomic weight can be obtained from the periodic table and this valency states can be multifarious there can be plus 2 plus 3 plus 1 states or maybe you know minus 1 minus 2 states and so basically one has to be aware of at what stage this is a electrochemical dissolution is happening is it a divalent association is it a trivalent or a those kind of things have to be taken care of while doing electrochemical machine. So, let us actually look at a little slightly different aspect of this theory and what I would like to now go ahead and work out is how ions or how solutions would behave at the interface of interfacial boundary of a solid and a solution. So, whenever there is a solid which is immersed in a solution there is almost always the formulation of a certain layer of charges which is also known as the dual layer of charges. So, automatically by tendency you know by the natural tendencies the metal which you are immersing in a solution would try to bleed out ions and it would retain electrons and there would be a ion electron pair which is thus generated with the ion floating in the solution and the electron on the electrode and then there is going to be a very thin layer of a dielectric high dielectric like water which is separating both these ions and electrons and not allowing them to intermingle again once they have been liberated. So, each ions thus formulated as a bunch of water molecules around it and it does not let the ion go back and take the electron from the metal surface. So, it is very important to somehow see the characteristics of such ions may be positive and negative in a solution and how they are transported and such a transport theory was for the first time proposed by you know which came as Debye Huckel theory of ion transport and so basically we want to look into that aspect before starting with electrochemical machining because a corollary of that which is the zeta potential of any surface is very important for the process of electrochemical machining. So, let us see what happens when strong electrolytes are completely ionized and their ions are not entirely free to move independently of one another through the body of a solution except when this is infinitely dilute. So, the following situations may happen. So, let us say there are positive ions in this and there are bunch of different negative ions and each of these positive ions are formulating a cloud of negative ions around it something like this. So, these are cloud of negative ions around it. So, the first effect that one can imagine intuitively is that the ions will move randomly with respect to each other due to fairly violent thermal motion. So, this is also the Brownian movement that the ions would move due to their ambient thermal energy which is a function of the temperature state at which they are in they would actually move randomly with respect to each other. And then there are going to be coulombic forces between opposite kinds of ions like for example, in this case let us say the positive charge centers and the negative cloud around it of negative ions around it there are going to be coulombic forces of attraction which would lead essentially to the assembly of these charge clouds around the positive central charge systems or vice versa. So, this kind of leads to a time averaged ion atmosphere of one kind with respect to a central ion of the opposite kind in this case it is a positive central ion and the time averaged atmosphere is a negative ion and this is the distribution which will almost always happen when you pour you know such a ion pair or an ionic solid into the governed by coulombic forces into a solution like NaCl in water. So, Na plus and Cl minus and then water comes in between. So, water molecules kind of because they are high dielectric they get into and engulf the Na plus and the Cl minus and they do not they seldom allow them to come together. But then what can happen is because there is an overall positive charge center in the Na plus and overall negative charge center in the Cl minus there can be a assembly in a manner. So, that there is an average atmosphere of Cl minus around Na plus or vice versa. So, that is what we are meaning by this coulombic forces and then supposing you make an external electric field apply to such a system where this let us say is the positive side this is the negative side. So, all the negative ions will start moving in the positive end and the positive ions of course, will start to move in the negative side. And therefore, movement of such ions under an external electric field first of all will be very slow and the atmosphere starts moving in the opposite direction as in this case you can see the negative ion atmosphere moves to the positive side and the negative the positive central ions start moving to the opposite that is the negative side of this field or potential which is created by two electrons. So, therefore, there would be a continuous disruption and reformulation in the ion atmospheres with respect to the central ions. So, for example, when they start moving these negative ions are going to get reformulated in the cloud of the second positive ion right from first positive ion it moves to the second positive ion so on so forth. So, therefore, there is an assemblage of charges which kind of disrupted from the ionic environment of ion 1 into the ionic environment of ion 2 and vice versa and so that happens all way throughout the solution. So, therefore, there may be many effects like electrophoretic effect which is essentially the movement of the charges across a medium over a potential externally applied to the system and there can be also viscous drag of the atmosphere because mind you these all moieties charged moieties are present in solution. So, therefore, if the positive center is moving ahead and the negative center is trying to move in the opposite direction it is obvious that there would be viscous effects or there would be shear between the layers of the solution which is containing these ions in turn. So, there would be a viscous drag which is associated with the forward motion of the ion through this whole so called atmosphere. So, all these parameters need to be included in a model where we can really estimate what would happen to the layer of moiety which is formulated across a metal electrode ok. So, let us look at how we will be able to in a simplified manner model such a situation in a solution. So, let us look into the formulation of this sort of ion transport equation which is also known as the Debye-Hacken equations. So, let us suppose there is a positive charge and a single positive charge and it has a environment made up of both positive and negative charges and at a distance of at an infinite distance from this charge of the charge density of the positive the number density of the positive or the negative charges of the environment of this positive charge are n plus 0 and n minus 0 per unit volume right. So, this is the positive or negative charge number density meaning thereby number per unit volume of this ion of interest central ion of interest which is a positive charge. So, supposing if we wanted to find out a point A here in the near vicinity of this positive charge this central positive charge of interest here the amount of work that and let us say at particular A there is existing potential psi defined by a function. So, this psi is the potential at a point near the central charge. So, the work done for a positive by the system for let us say moving a positive charge is actually given by the charge itself let us say the charge as a valence is z plus. So, z plus times of electronic charge epsilon this epsilon as you all know is 1.6 10 to the power of minus 19 coulomb electronic charge right. So, the total charge on the ion times of the potential similarly the work done for moving a negative charge from distance infinity where psi is 0 actually all the way to this point A. So, from for moving a positive charge from infinity to A negative charge moving a negative charge from infinity to A would then be given by minus z minus epsilon psi psi is the potential at A z minus is the valence C on the negative ion and E of course, as you know as the electronic charge. So, that is the amount of work which is done in case of a positive charge or negative charge come from infinity to the point A close to the central ion of interest. Now, if we look at so therefore, there would be a possibility of a charge distribution at the point A which can now be given as n plus and n minus and these mind you are numbers per unit volume number of positive charges per unit volume number of negative charges per unit volume. So, we are concluding here that the ion which is the central ion of interest is assembling its own charge atmosphere around it and at a point A the numbers are n plus and n minus of positive and negative charges per unit volume assuming that at point in space which is infinite distance from the central ion the distribution of the positive and negative ions are n plus 0 and n plus n minus 0 in terms of numbers of charges per unit volume. So, and we already know what is the work done for moving one charge of a certain value of a certain charge from infinity to A. So, there is a correlation which exists and I am not going into the details of that correlation between you know the numbers which are at the point A to the numbers which are far away or at infinite distance from the point A. So, that correlation actually emanates out of the Boltzmann distribution. So, from Boltzmann distribution the n plus 0 number density near the point A is actually equal to n plus 0 added infinity times of exponential to the power of minus the total amount of work which is done. So, z plus epsilon psi by k t and this is also a function of the absolute temperature in which the system is installed and similarly the n minus at the point A mind you these are number densities at point A these are number densities are infinity point infinity. So, n minus 0 e to the power of z minus epsilon phi psi by k t. So, k is the Boltzmann constant and n plus or n minus are the numbers per unit volume near or at A n plus 0 n minus 0 numbers per unit volume at infinity or at infinite distance. So, the total electrical density the total electrical charge density near A or at A can be given as the numbers per unit volume at A times of the amount of charges let us assume the charge on one ion is z plus epsilon minus the number of negative charges per unit volume times the value of the charge z minus e on the negative ion. If we substitute the values of n plus and n minus from this set of equation one earlier we can get this as n plus 0 z plus epsilon times of e to the power of minus z plus epsilon psi by k t minus of n minus 0 z minus epsilon times of e to the power of z minus epsilon psi by k t. So, that is the electrical charge density at the point A and if we just apply Taylor series here and just assume that the higher orders are negligible x square by factorial 2 plus so on so forth and we assume that the higher orders because of the low value of x are negligible. We can write this equation number 2 in the following manner. So, you have rho at A the overall charge density at A written as n plus 0 z plus epsilon times of 1 minus z plus epsilon psi by k t minus of n minus 0 z minus epsilon 1 minus z minus epsilon psi by k t and therefore, this can further written down as n plus 0 z plus epsilon minus n minus 0 z minus epsilon minus of n plus 0 z plus epsilon square psi by k t minus of n minus 0 z minus epsilon square psi by k t. So, this of course, is 0 because at infinite distance we can assume the principle of electron neutrality to exist and this becomes 0 and so, the other term which can be taken care of is basically minus n plus 0 z plus epsilon square by k t minus n minus 0 z minus epsilon square by k t times of psi. So, if we assume that the charge densities of the positive and negative kinds are same at infinity which is actually true because of again the principle of electron neutrality coming into existence and this we assume to be equal to let us say n i. So, we formulate a system where i is a set of all positive and negative charges. Let us say i varying between 1 and n meaning thereby if it is exactly half 1 to n by 2 can be the positive charges and by 2 to n can be the negative charges so on so forth. So, therefore, we can write down this charge density equation rho a as in a very simplistic manner as sigma n i z i square. Now, I am actually getting rid of all these pluses and minuses in the subscripts and representing them by i's. So, n i z i square square of epsilon times of potential function psi by k t. So, that is the density of the charges the overall charges at a point a in space close to the central ion of interest. So, we somehow need to be able to derive the potential function which exists at a near that central ion of interest owing to the charge density which is around it. And in the next step what we are going to do is to utilize the Poisson's equation in the space coordinates and try to find out that at least in the CGS system the gram centimeter second system how this equation can be used for determining the electrical field at a point a because of the complete amount of positive and negative charges with densities n n i where i varies between all the positive and negative charges close to the central ion of interest. So, the electrostatic potential and charge density are related by the Poisson's equation as del 2 psi by del x 2 plus del 2 psi by del y 2 plus del 2 psi by del z 2. This is the special all second derivatives space derivatives and that is actually equal to minus 4 pi charge density which is actually the charge density at a rho at a by the dielectric constant. Here psi is the potential at a rho is the charge density at a and d is the dielectric constant of the medium. So, we want to somehow be able to solve for this equation to find out a relationship between psi and all these other terms like charge density dielectric constant and also of course this space term. So that you know psi can come as a function of the special variation and also the variation of the charge density between different shells around the central ion of interest. So, what we will try to do is to just use a simple conversion technique to convert this whole you know equation into polar coordinates. So, here what we assume is because there is a central ion and you know potential function really varies as a function of distance r from the central ion and so somehow we have to convert this whole equation into polar coordinates or spherical coordinates and then assume only variation along the radius vector r or we assume spherical symmetry. So, I am not going to go into the derivation of it, but the approach can be represented here let us say you have a Cartesian coordinate system x, y, z and you have a radius vector here r. So, you have the first projection of the radius vector as on the x y plane. So, this can be projected by let us say an angle gamma.  So, the x component can come out to be r cos gamma sin theta and y component can come out to be r cos gamma sin theta or cos theta sorry cos theta and then of course you know that the z component is already r sin gamma. So, if you were to change this whole form of Poisson's equation into polar coordinates you will have to just represent psi by differentiating with respect to r gamma and theta using the chain rule and then assume spherical symmetry. So, the variation that you are assuming is only along r. So, this whole equation now gets converted or changed into the form 1 by r square del by del r times of square of r times del 2 or del psi by del r and this is equal to minus 4 pi rho by d. So, this is the spherical coordinates or you know this equation is spherical coordinates or polar coordinates assuming that there is a spherical symmetry and there is no variation along the angle gamma or theta the only variation is along the radius vector r. So, we want to now be able to solve this. So, that psi comes as a function of r rho dielectric constant d so on so forth and it is very amenable for us to now try to find out what is the work done by a charge at infinity to come very close to the surface in question which is actually a where the potential is psi. So, here let us try to solve this differential equation which has been obtained 1 by r square del by del r times of square of r del psi by del r equal to minus 4 pi rho by d and we already know that the rho has been illustrated before in an equation which you formulated earlier as minus n i z i square square epsilon potential functions i by k t. So, therefore, this can be represented as 1 by r square del by del r times of or del by del r of r square del psi by del r minus 4 pi by d and the minus goes away n i z i square epsilon square psi by k t. So, if you are to just take this portion stand alone and consider this to be square of small k the capital K of course, here as you are seeing is the Boltzmann constant. So, we will not go into that the small k. So, the small k square can be represented as 4 pi d sigma n i z i square epsilon square by Boltzmann's constant capital K times of t let this be equation 3 and we can represent this equation 1 by r square del by del r of r square del psi by del r as square of small k times of potential functions i. So, this of course, is a standard equation with the standard solution and there is also a general differential equation it is not partial anymore because on the one variable is involved and the solution to this the standard solution to this comes out as psi equal to some constant a times of e to the power of minus small k r by r plus some constant a dash times of e to the power of small k r by r. So, that is how the standard solution of this equation comes out as. So, we will take the solution and try to investigate what these values of a and a dash r a prime r based on the boundary conditions that are imposed on to us through this problem. So, here the first condition that we can actually think of is that the potential functions i is actually 0 at r equal to infinity right and therefore. So, psi infinity is 0. So, if you consider psi to be equal to a e to the power of minus k r by r plus a dash e to the power of plus k r by r meaning thereby that if supposing this whole psi equal to 0 be true at r equal to infinity a dash automatically becomes a 0 otherwise this term will you know be undefined by undefined.  So, therefore, overall the equation can be 0. So, therefore, a dash is 0 from the boundary conditions and psi becomes equal to the constant a to the power of or e to the power of minus k r by r. So, that is the solution for the potential function at a close to the central line of interest which is a to the power of minus k r by r. So, we already know that from the previous equation that charge density had been earlier defined as a function of n i z i square epsilon square psi the potential function by Boltzmann constant k times of t and. So, we can actually substitute the value of psi that we have obtained here to obtain the charge density at space close to that point a as minus a e to the power of minus small k r sigma n i z i square epsilon square divided by Boltzmann constant k times of absolute temperature t times of r just a substitution. So, that is what the charge density value comes out to be or in other words if we were to involve small k into picture you know that small k was defined by equation 3 here. So, therefore, we can say that this whole term can be written down as a small k square by 4 pi times of d e to the power of minus small k r by r.  So, that is how the charge density would equate to close to the central line of interest at a point a very close to it. We will try to now find out. So, we kind of coming at the end of this lecture, but in the next lecture we will try to find out what is the value of a which we would like to investigate and finally, the potential function will come out once the value of a comes from a certain condition that we would do in terms of principle of electroneutrality of charges around the central line of interest. So, with this we close today's lecture and we will try to solve this or take it up and solve this further in the next lecture. Thank you.


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Hello everybody, my name is John Hammond and welcome back from the YouTube video and man, it's been a while It's been a while since I posted a video It's been a while since I posted a power shell video and I have heard you I've read your letters You haven't sent me any letters, but I've read the comments and I know you guys were really wanting this So hopefully I'll be back at it back on the saddle and here we go This is power shell video number two. So we are gonna talk about output and some file system operations So without further ado, let's get to it. We know how to open up power shell You can simply open up your little start button there and search power shell.  We know the command. Let's now get child item and That will display the current directory listing or what's in our current directory And we know that's from our prompt visible where we are currently If we were to move with anything within that we are using an relative path If we use a period forward slash and anything that needs an absolute path includes the entire file structure C colon backslash or where we are from the root of what we're working with so Simple recap, right? That was the get child item command. We know that that is Aliased as something that power shell. Let's us do with the LS Kind of alias here and we've seen dir so LS if you're more Linux kind oriented dir for more old-school windows cmd.exe some DOS days and That's our output nice and easy super small We've done that before now we do want to learn how we're actually going to interact with the file system How we can do those copy file move file those regular things you would do in a GUI or in the file browser and explore So let's dive into that but before we do I want to chime in how we can actually Output some of this output in a different way the things that power shell lets us do so let's get started with that I will get child item again And we know through the pipeline that vertical bar just kind of the shift form of the backslash your keyboard Above the enter key that will allow you to transfer some of the C sharp net objects that we've seen as The result into that previous command into something else something new So I want to show you this kind of family of command let's Format hyphen and then whatever you want to format that output in so it's pretty simple It's pretty easy if you're to type format hyphen and I just figured this out I don't know if this is maybe my updated Version of windows to the power shell version I'm on right now But if you hit control spacebar, it'll show you some of the options of the things that you can actually use It'll help autocomplete what you're trying to work with it'll even show you a little bit of the help information What parameters or arguments you want to pass to it what you can pass to it and you can use your arrow keys Just kind of move around and navigate this little quick on the fly help system inside a power shell So by default the output that for that power shell will give you is format table So if I were to pipe this to format table, you see the exact same results we had earlier That's kind of boring and lame you can change I think how you Actually have power shell default to show you information, but the other options that we have are format wide and That will showcase some of the output and just kind of a tabulated way But now if the actual kind of headers the rows and columns there You can see it's just giving us the name of the entry not any of the other properties that we might like But if we wanted to see a lot more of the properties one cool thing we could use is format list And you can see that here of the other arguments that it might take maybe zooming on a specific property But format list works well for us because it will return each Entry each object that kind of our command that finds for us and give us a little bit more of the properties You can see link type and target and maybe we didn't see that by default when we ran get child item yeah, we didn't see The target and even it had a last right time kind of by default This will show us last access time and creation time and maybe some other interesting information This is a neat trick that I really want to show you because with format list You can actually get more properties that you may not have even known that that object might carry with it Let me show you this if you run get child item with format hyphen list and then add an asterisk at the end Suddenly you get a ton of information for each of those objects the attributes that might come with it I guess a parent directory a base name Everything that might be relative and pertinent to that object This is just kind of specific to this file system that we're looking at right now You can see that ps provider what we're really looking at But if we were to scroll through that we can see there's a lot of stuff that maybe you hadn't seen before So that's a good way to kind of track down some properties Maybe you hadn't seen before if you want to do a quick shorthand way to do that get child item The alias for format list is just FL and then FL star Here's all of the cool things you can do you can assume format wide is FW and that does that just as well And remember if you don't know any of these aliases you can check out get alias and That will return all the information for you funny thing the alias for a get alias is gal gl and Remember the power shell is case insensitive So it doesn't matter if you were to run get hyphen alias in all caps or whatever the case may be gay Al I don't know That's something that you can keep in the back of your mind power shell does not care about what Semantics you're using case sensitive case insensitive doesn't matter caps or lowercase So because we can use get alias and we can track down some of these Maybe commands that you might use in another language other language is not the right word But if you're on another operating system, you're kind of used to that old-school CMD.exe style or the linux style LS dir maybe some of those File system commands that you're used to or anything that you would just normally type in out of habit like echo like echo Literally just let's display some output on the screen echo The classic right we've just done that But what did echo come from you can gal echo just as an argument and you can see that that is alias to write output So if we were to simply write output It has the exact same effect because it's simply an alias kind of a recap on what we talked about in the last video but It helps me segue into a new topic and conversation because output is something that you can Control in the way that you're using and interacting with PowerShell right now We're working with PowerShell in just the console PowerShell.exe or this this program that we have open in the command line But how PowerShell is ran or invoked its host environment might differ We might get into PowerShell ISC as we will in later videos Or maybe it's running in a web browser because you've done it with some DLL magic output will allow us to kind of Change up what we're working with and how we can see things So let me actually dive into that if we were working with our alias output or our Python purist way Let's run get child item. We can pipe that to out And out is what we can use to kind of modify this and I'll use that control space bar to get some kind of Suggested auto completions for us. We could out host Just as we've seen before regular default output But it comes with some other things we can output if you want to get it as just a string Now we're not seeing the C sharp object anymore, but we're actually having them converted to a string Just regular kind of double quotes as you would expect in any of the programming language or more of a text-based console standard output standard input kind of the Linux way or This has other great stuff to us out null That's kind of like redirecting to forward slash dev forward slash null or kind of Squelching the output so you don't get to see it. That's might that might be handy for you later down the road Additionally, we have out file. So we've seen before and maybe some old-school Dostays or cmd.exe you can use the greater than symbol or the kind of redirection here. Let's call this Directory dot text right Now if I were to check that out, we've created a file directory dot text And we've just redirected that output or the command. Let's kind of results here Let's actually check out the information or the content inside of that Directory dot text I'll tap complete here and there is our output interestingly enough though It stored it when directory had no value to that's kind of a little funny Easter egg You can see the length of that file is zero at the time of Kind of reading the file, but if you actually check out on the file system It's filled with the contents of that file. So interesting thing. Maybe maybe you'll get a kick out of that. I did anyway So that's using the regular old-school redirection powershell lets you do that just as easily With piping it to out hyphen file and you will of course need to supply a parameter, right that path following it So let's call it again directory dot text Check out what we're working with and it's the exact same file size. It's the exact same file So we can open it up in notepad directory dot text and you'll notice we have still the headers And everything that we would have expected in a regular powershell output Because it's format table if we wanted to see format list or format wide We could use just that or select to move kind of our properties out as needed Those are other things you could do with it But those are the ways you can format your results in powershell and how you can output to some of them Before I kind of close off on that I do want to show you out grid view because you guys might like this that might come in handy This will give you kind of a quick GUI interface where you can actually scroll through some of the things that you're working with Click on them and do interesting things with them or if you had a ton of results That were just taken up a lot of space you have a little filter up here where you can search for things Like okay, I only want the entries that contain the letter o or whatever the case may be or a or Anything that you might like you can especially add criteria for some of these properties And you can verify whether or not they contain something or do not contain or start with or equal something And that will help you kind of narrow down your results if you have a huge data set that you're working with So that's out grid view. I think that's kind of handy Okay, we talked about right host We talked about how we can output into a file or a grid view or any of those other out Solutions and formatting them in a different way. Now, let's work with that directory dot text file that we've created so If you are again more Linux minded kind of like myself, you're used to the move command and the Power shell calls that move item And if you didn't know that again because you're used to that kind of structure and syntax You could just check out that alias gal mv and you'll see it tells you that is in fact move item Same thing with cp to copy right check out the alias for cp that command is copy item So if we wanted to kind of move this item Of the directory dot text we can bring it into our desktop Just simply running that command has the effect if I were to minimize you can see my directory dot text is just there Get power shell back open Run ls or get child item. You can see obviously it's not in this director anymore But we'll use our relative path dot forward slash or dot backslash Check it out. Now it's in our desktop because we just moved that if we wanted to copy item Super simple, right? Let's take a directory and again using a relative path the symbols two periods for the parent directory Let's just move it up in the file system Now if I were to move back I can ls and I have a copy of that directory dot text right there If I didn't want that file anymore, though Maybe you're used to the rm command if you're linux minded or you're used to the dell command if you're windows minded You can run remove hyphen item in that power shell pure way. Let's run remove item on directory dot text And now that's gone. We don't have that entry anymore. We don't have that file Some of these directories that windows likes to put here kind of by default I think are stupid and I never really use so we could remove some of those if we wanted to and you might be used to rm dir In power shell there is no difference between a directory that we're trying to remove or a file that we're trying to remove It all just calls it an item. So we can simply Remove item What is that one called save games? Let's do that This might ask us.  Yes, or enter y and work with it or any of these other options that power shell will give to you If you wanted to figure out, how can I just get it to shut up? Like stop asking me that check out the help for it It'll show you the aliases that we're working with And i'll try and scroll up here One of these options is tat confirm where it says, I don't care Do it do it all and same thing with tack recurse and tack force if it says like hey, we're not able to do this Whatever just ignore it We can try some of those out. So let's remove item tack confirm Oh, we still need to work through it. Okay. Let's just use recurse instead Oh, can't use some of those. I guess i'm not the administrator I'm not able to remove some of the sensitive i and i files whatever Again, that is the commandlet that we're using though remove hyphen item. That'll take the place of rm dl and rm dir So those are the commandlets that I wanted to show to you in this video Again, super simple stuff. We're just kind of navigating around the file system We're checking out how we can output and format our information within power shell Next we'll move on to some of the good stuff. We'll get into scripting We're getting the profiles variables execution policy stuff like that But we got to get this beginning stuff out of the way. So thank you guys for watching I hope you enjoyed this if you did please do like comment and subscribe There is a discord server that you can hang out and all of us are trying to learn trying to get better Just jump into the cyber security scene. Please do click that link join the discord server It's a great community so many smart people and they're much smarter than me So, uh, I'd like to see you guys in the next video. Let's see you on patreon. Let's see you on paypal All the other things. I'm really bad at outros. Thanks for watching You