OK, very good afternoon to each one of us present here. We are going to debate and discuss a very important topic, closing gender gap in South Asia, and why is it so important? Why is it so imperative? Why is there a need to do that now? I have a very, very eminent panel of guests with me, each one of them, a leader in their own right, each one of them, to make an important point. And perhaps we will go away with very key takeaways from here. I begin with my extreme left. OK, we'll begin with my extreme right. Ms. Kiran Bedi, founder and secretary general of India Vision Foundation. I've been a fan, ma'am, all my life, and welcome to this panel discussion. It's my honor to have you here. I have Keshav Murugesh, the group chief executive officer of WNS in India. Ms. Kavita Ramdas, who represents the Ford Foundation here, Ms. Mehnaz Aziz from across the border, chief executive officer of Chandru's global network in Pakistan, and of course, Dilip Chenoy, the chief executive officer and managing director of National Skills Development Corporation in India. Thanks to each one of you for being here. This is a very serious topic we are discussing, and I guess it's only fair that we begin with opening remarks from each one of you. I'd like to begin with Ms. Bedi first and perhaps go around the discussion. We're talking about the gender gap. We're talking about what breeds it. We are talking about the economic outcome of it, the social outcome of it. I want to first to your brains a little bit on it's not new. It has always existed. We are obsessed with growth levels. We are obsessed with fiscal deficit levels. But when it comes to this gender gap, nobody seems to be losing sleep. Isn't that something that concerns you? Why would they? India has a resource dividend, and every person is not needed. India has a huge population dividend. You're not Israel, where every woman is needed even for the armed forces. There is no compulsion that every woman becomes an earning member. If today a woman is becoming a member of the economic world, she's out of expression of her education. She's out of her own talent. She's out of her own will or passion of some of her parents. So I think there is no, India does not have a compulsion for women to work. They could as well let women be back at home and let them be. Probably it might just soothe the society much more. So I'm not being generalist from that point of view, because I straddle to three segments of gender. For me, when you talk of gender gap, I look at it, which gender gap? Whose gender gap? Who are we addressing? There's a top gender gap, there's a middle gender gap, and there's a bottom-level gender gap. The bottom level is, if you begin with the bottom level up, then it's 60, 70, 65% of Indian women. So let's say you're talking of millions of women who are not even having access to opportunities. They do, some of them may not have access to a nearby school. They have no access even to a dispensary for healthcare. They may, for them, vocational skill is out of the job. The vocational skill is not next door, because that's where my learning comes from, where I work with them, as will do without them, because there is no compulsion. So where is the compulsion coming from? Parents, social networks, NGOs, saying come out of the house. There is no compulsory door-to-door search. Why aren't you into education? The girl child, the girl is not going to school, because she doesn't have, she has to fetch water. One policy across, then you may leave out many sections. So my opening remark would be, when you look at gender gap, you cannot bracket all women in India, or even in South Asia, as one sec, one constituency. There's a top level, where probably we may be sitting here. There's a middle level from where we came from, and there's a bottom level, who we work for today, because we think it's time to get it. That's an important point, and I will come back to you, because you mentioned access to education, access to primary healthcare. There is access to being born. I mean, that is a big debate that is doing around the world, and we will talk about that. But Keshav Vargish, Ms. Bedi made a very important point about strategizing. There are three levels of gender gaps. We perhaps, when we talk to you, you will perhaps be addressing either the mid or the top level. How much time will it take for the industry to address the bottom level?  Women actually perform exceedingly well in our business, have taken leadership positions across. And for me, really, it's an opportunity, the fact that India, for example, even if you leave out in South Asia, India alone has 400 women. So for me, my focus all the time is, how do I keep taking my business model deeper and deeper into the hinterland of the country, and accessing more and more of those people. And as Kiran said, I think the most important area of focus has to be education. And obviously healthcare, education, as well as access to the government is important. But I think the education part is the most important, because when you educate a woman, you don't really educate an individual. You end up educating a nation, a country, a family. And we've seen from our experience that by essentially driving initiatives inside the company, we're able to achieve some of these outcomes. And I think it has to be done in terms of not waiting for the government or somebody else to come and tell you do this, but really saying, here's an opportunity, here's an opportunity I need to get after, and then focusing on key initiatives to drive some of this, some of this. And again, if you go five years back, you will see that I think a lot of the focus around gender inclusivity in India probably started getting surfaced because of the need for managerial talent, right? And maybe accidentally India went down that wave because there was this need for more people, more qualified people, and that's where women started coming to the fore in our business at least. But since then, I think all of us as companies have focused very strongly on creating policies, processes, great working environments, safe work place kind of environments, such that as a result of that, I'm really proud to say that at this point in time, the Indian IT industry of the total population, 24 to 30% of the employees are women. And for the business process management business to which I belong, 35 to 42% are actually women. So I'll stop here, but the reality is, I think it's a lot to do with how you drive the model inside your company. I'll talk a little more about some of the things that we do a little later. No, I also want to come back to you and talk about policies and practices that will get more women in the workforce and will also perhaps keep them in the workforce. I think women drop out because of very, very increases. I like the point that you mentioned about IT. Those are numbers. We're obviously proud about 25% of workforces women. It's a number to be proud about, but you know, Kavita, I know you feel strongly about this and we were discussing this just a while back. The point that Ms. Pethi made about access to education, access to healthcare, we've been speaking about this, access to being born. I mean, everything boils down to that. Yeah, although I'd like to begin by saying, first of all, I'm really glad to be on this panel and I want to remind us that it's not a panel about women's rights. Sure. It's a panel on gender parity and gender gap and I'd like to begin by saying something that might be a little bit controversial, but I would like to put it out there. I think you have to understand first what we mean when we use the term gender. And I would argue that gender is not something that is defined by what we have between our legs. Gender is defined by what we have between our ears, which is to say that gender reflects a mindset. It is how we conceive of and construct identities of both women and men in our current space. And in the current space that we exist in, I would say both men and women have a limited frame within which they're allowed to function. What do I mean by that? What I mean by that is that there is a set of expectations that both women and men hold about what it means to be equal. That's right. So I think we actually have this idea which has driven the women's movement for a very long time globally as well as in India, which is that all that it actually takes is, we have to scramble to be equal to men. Now, if you would stop and ask men what it's been like to actually be in the positions they've been in, not to have the luxury of being able to say, you know what, I'm not really interested in being the breadwinner for my family. I want to be an artist or a painter.  I want to take paternity leave and nobody's offering it to me because, I'm a man.  Although I think it would be important for us within the women's movement, all of us who care deeply and passionately about women being treated better in our societies, to recognize that patriarchy is a system that affects both men and women equally. It restricts the freedoms and the opportunities to fulfill our greatest potential on both ends of the spectrum. And if we're to have a chance to be able to reimagine a world in which all of us have more chances and more opportunities, that has to be a world in which both girls and boys can dream about what it is they're really hoping to aspire to. So then if you come back to this question of the right to even be born, you know, do you want to be born into a world where your opportunities are so severely limited from the get go? And do we understand why people are choosing to abort female fetuses? So rather than sort of, you know, I think as we did with female genital mutilation 10 years ago, there was this kind of, oh, it's a cultural thing. People in India are so weird.  No, Kiran made a very important point. This is about economy. We live in an economy where there isn't any pressing need. We have a surplus of labor on multiple fronts. You have a girl child in a context where a poor family can barely afford to be able to pay for a dowry or to have her get married. You have a real set of economic constraints. So rather than sort of simplify this to sort of like, oh, it's some cultural thing. And we need to kind of change, it's not that we don't need to change mindsets, but I would simply submit that I think both men and women have a long way to go in sort of throwing off the shackles of what I would call, you know, a system in which we've both been oppressed. And I think it's time for us to now start thinking about a different world, one in which we can all create a new vision of what we'd like to be together. I like the point that you make. I mean, are we aspiring to be men here? Are we aspiring to share your burden, your sorrows? Perhaps not.  You come from Pakistan. I know you want to speak about education in particular, but just your opening remarks on the debate so far, Ms. Medhi talks about the economic imperative of not having women around. Keshav speaks about how the IT industry is perhaps doing a lot more because I think they realize at one level the kind of jobs that they have, the kind of work that they need to be done, has to be done when you get the rest of the workforce. Kavita makes an important point about are we aspiring to be men? Perhaps not. Where are you in this entire debate? You know, as Ms. Medhi had rightly pointed out that there are layers that we need to look at, you know, and in Pakistan, I will talk about Pakistan and I will talk about education.   And I have an image here very important, you know, Malala who was recently shorted in one of our tribal areas by Taliban's because she said that, you know, I do not agree with Taliban's and I want my schools. Taliban's are hitting at schools in some of the areas, not the entirety of Pakistan. And to silence her, you know, the biggest threat to some ever-ever's actors in Pakistan is girls' education because with the result, the girls and women are really pushing back and now our majority of women are in rural areas. What we are finding out is this that, you know, the illiterate mothers really are wanting their girls to go to schools. They are fighting tooth and nail. You know, the state is not responding in a manner that they should be responding to. You know, education is a genderless matter and we are trying to bring gender back into it because most girls are out of school, not out of choice, not because they are pushed back to work at home. Obviously, you know, our religion is made as an excuse or something else because there are no schools. That's right. And it's a fallacy that people don't want to send their girls to school. So we are there. We are at a very critical juncture, but the thing is this, like, you know, I work in one of these conflict-ridden areas, Buneer, right next to Malala's district, whereby girls are, and it's very, very traditional. Like, you know, you're not allowed outside of traditional tribal, Pathan culture, but girls are sitting in boys' schools because there are no girls' schools. But there is a need. And the other thing that is happening because the government is not responsive, the government is gender-blind. So what is happening is this, that we are getting this whole influx of private sector schools. You know, low-cost private sector schools wherever there is a girl available who has gone through secondary school to be employed as a teacher, there is a private school that is erupting. So in Khaybar Pakhtunkhwa and in Punjab, 70,000, Khaybar Pakhtunkhwa around 40,000. And the largest employer female, you know, employer force. So it is that, you know, it's just like this, the rural women are now at the forefronts of this change. And the women who have fought to get educated, now who are in their early 40s, are the strongest allies in any kind of change that we will see in Pakistan.  And so this is a very positive story in Pakistan. We, on the other hand, you know, are responding. The state has responded by having a law for 100% literacy. We are working on it. And we are trying to make it more gender responsive. And there is a very large education campaign on by one of the media houses and also talking about girls' education and all that. So extremely important, but also I would like to mention here that this is the story of the rural women, the resilient rural women of Pakistan. But on the other hand, women who do get a chance to get educated in professional colleges are doing much better than boys. You know, there is like 55% girls and 45% boys, but they do not get into professional jobs. They want to get married and sit at home. You know, doctors, lawyers, anybody like that. But that is where the social fabric comes in. Yes, they're expected to do that. You know, our problem, when I look at Pakistan, our problem is this, that our middle class, our intellectual class, the women are holding themselves back for the convenience of subservience. So the story on the rural side is extremely bright and I think they are the ones who will write the tide of change. That's a very important point she made. I mean, you can be the most professionally educated person around, but as a woman, you can, you know, you can make the choice of holding back and you will not be questioned. Imagine a man who's a trained doctor sits at home to rare a child. I mean, what will the world do to him? Dilip, before I open this debate to other people, I'm gonna come to you because we've spoken about survival. We've spoken about education. We need to talk about training. I mean, the economic imperativeness of having more women in the workforce also has to do with lack of training. Do we have enough skilled trained man slash woman power? Thanks, I actually want to go back to the point that Kavita made and say that as a country, and it might give a different dimension to the point that Dr. Bedi made in terms of jobs and reliability. If you look at the next 10 years, it is estimated that we would have 800 million people in the workforce by 2022. And a rough calculation shows that 200 million would be graduates, right? And 500 million people would be unskilled. And there, actually, when the prime minister put this target of skilling 500 million people, we asked the question, are there 500 million jobs or could there be 500 million jobs in the economy? And we actually came to the conclusion that there are more than 500 million jobs in the economy. And what he found was that because of the lack of availability of people, industry and people were making choices to invest in capital rather than hire people. Because of lack of trained people, they were hiring over-qualified people and distorting the labor market. So I think both for men and women going forward, there are at least, which we have documented 347 to 500 million jobs that are there. And the interesting part is that only 12.8 million people joined the workforce. The labor participation rate is less than 43%. Women is 26, men are 84, so there's a kind of a skew there. So if you're going to fill those jobs, we need to actually ensure 50 to 60% labor participation and move women out of agriculture. So unless we do that, the economy is not going to grow. And if the economy grows, so the growth is essential to actually getting gender equality, whether it's in the whole economy going. So the first point. The second is that there's a conflict between tradition and modernity. The tradition comes up with all what Kavita was saying. I think modernity is reflected in this room. But there's something happening quietly along. There's the urbanization of mind which is happening across the country, driven by the access to television. And that is creating an aspiration. And that aspiration is now letting women to say, okay, we need economic environment, we need jobs.  And there are two types of people. The government also has recognized this. And at the ground level, and Dr. Biddy talked about middle level, lower level, and top level, there's also regional disparity. There's the Kerala and the Northeast, which are matriarchal societies, which have different indicators than the rest of the country. And if you look at Asia, each country needs a different thing. So the democratization of information, of the urbanization of mind and the democratization of information where things are now being available and soon it's going to change. It's actually changing the social fabric and more people are aspiring for jobs. More people are aspiring to become part of the economic activity. But the problem is a structural problem. It's only 7% in the organized sector. 90% or 93% in the organized sector. If you look at the women participation in workforce, out of the 140 or million, it's fascinating that 138 are in the unorganized sector. In the organized sector, where we've got Murgesh talked about and the others talked about, the number is there. And there's some interesting developments happening. This last week, there were three or four public sector chiefs who were women who were put in there. Yama is hiring 300 women engineers. The percentage of mechanical engineers and engineers is going up. You see, that's all been driven by the social change. So the problem, the real thing here is, everybody talked about how do we improve access? So education is there, but in India, there's another problem. The women's participation in the workforce is declining because it's staying longer in education, right? The second thing is that you talked about, there's an under-accounting of women in the workforce. There is a kind of a withdrawal from the workforce which you talked about. So the statistics also is kind of challenging. But then, the big thing is that how do you actually bring about change to enable that to happen? Is it small things or is it different things across the whole chain from birth to life to after that and interventions at all the space? I think the biggest challenge here is to do something totally across the change. Individual things will not work. That's a fair point. Let's keep it open now and more interactive. I'm gonna come to you. He spoke about what do you do to bring about that change? Should it be across the value chain from birth to across the spectrum? Or should it be restricted to say one company, one man, one organization? How should one go really about this entire change? We all speak about it. But at the end of the day, it's be able to make the change. When I raise this issue that it's so stratified, when you do look at gender gap, if you don't look at it from this top level, middle level and bottom level, then you may miss out certain very large constituencies. Now, when I was addressing this issue, then I started to look at what is it? What is holding back the top level? Because they're also being held back. What's holding back the middle level? What's holding back the bottom level? And I looked at three key issues at every level. For me, what's holding back the top level is, men in India, sons inherit their parents' property. And daughters don't. Daughters don't. They do legally, but they don't do it emotionally. So the boy is born with the business as is inheritance. Girl could, but she chooses to opt out. And she says, I'll walk away with marriage or something like that. And nobody encourages her to think differently about it either. I mean, right from the very get-go, she's given a very clear message. She's a good daughter and a good sister. That if she's a good daughter and a good sister, she will refrain from asking for that. So here is not an issue of deprivation of opportunities. Here is what you said, it's right here, gender in the head, right? That's what she said. Secondly, we certainly have a smaller base. Supposing we got 100 people joining in, the women, let's say, would be 20. By the time they move up, they'll be left at five. And from the five, only one goes up to the corporate board. Whereas boys, 100 remain at least 90 out there. So out of 90, you will have 30 up there. So second is our base is small at the middle level. Third is the skilled. What holds them back is skilled, but holds them back by family responsibility. So even if the woman is an engineer, exactly what she said, what holds them back, highly educated woman, is a dual responsibility. In India, there's still a pressure of, this is as far as, that's why I was looking at, how do we strategize- Here is not just in India. I mean, the US has just had released figures on this whole thing. McKinsey just did a massive global report. And it's the exact same situation. This shift in terms of responsibilities within the home simply hasn't happened, even in the most advanced economies, with the exception of the Scandinavian countries, where state policies have essentially stepped in to provide that support, that otherwise, basically women carry on their own. That's what the solution is. So this was why I thought these three. Let's look at the middle level. The middle level is, she has access to opportunities.  Our vocational schools in India are just 5,000 plus 5,000 ITIs and vocational schools. China has 500,000. Look at the difference between vocational skill gap, which he's desperately trying to narrow. Mr. Shunoy, he's one man army in this country. But look at the gap, 5,000 plus 5,000. And as far as universities are concerned, we barely have 400 universities. Japan has 4,000 universities. So what are we talking about with this middle level access? Secondly is the larger issue of security. A middle woman, mobility is hit. Look, moment you have problems of rape, if teasing at night. The first victim is the middle class woman, the family doesn't let her go, or she says, I don't want a night job. So law and order security is a bigger issue for the middle level. Not as much for top, because she gets a cab, she gets a driver driven, chauffeur driven. The bottom level, she's anyway saying, doesn't matter, it doesn't matter. So third. It's a question of survival for the bottom level. And of course the third is what holds her back is family support systems. I've seen many women cops. The poor women had to, the women cops dropped out because the husband said, finally you gotta run the home too. So there isn't a backup which the social systems have provided. But what holds back the last level is, first of all, what's here and there? The parental, the basic attitudes. The woman still has a property, not as a person. And it's investment into her is still a drain. And then reproductivity. She doesn't have any rights on reproductivity. She constantly reproduces and because the child is, it has to be a son. So, and still is a domestic role. So unless we address these all the three areas separately in a focused way, you will continue to have this large gender gap from top, from middle, and from the bottom. You know, also one point that I would like to include here and from my experience from within my organization, like the middle class or the low middle class woman who is working. What I've seen is they're pretending their husbands are supporting them, but actually they are supporting the family. They are the ones who... It's a sin to be the bread winner for the family for a woman. You cannot be earning more than your husband. And I've seen this across organizations. I've seen it absolutely at the top level. They will shy from telling you that they actually... They don't even want to. I think it's a Pakistan syndrome. It may be an India syndrome. But they will never say... And the more they earn and the husband is unemployed, the more respect they will be giving to the husband so that his ego is not hurt. You know, so and they will be doing the double duty. He will sleep. He will not cook. She will go home. She will cook. She will be fasting the whole day in Ramzan and all that. And the kid is sick. She'll take the kid to the doctor as well. He will not do anything because he's the...  He's the God. He's the God of home. So that in itself, you know, it's innate that you know that husband is that husband. And you know, whatever I do, I will have to stay back. Another point from the Pakistani perspective, you know, we had a very good system at the local bodies. Elections of the local bodies and the local bodies representation, whereby we fixed the quota. This was in the last six, seven years. Fixed the quotas to 30% of women's representation and it worked very well. Now, there is the...  And that was done away with because of political patronage and, you know, and it's very stifling. So that push for that voices because right now in Pakistan, that space for the voice and my entire focus for Pakistan would be the resilient rural woman. Because I think, you know, if we start focusing on the urban woman, she's not done anything for herself or the rest of the women as well. True. And perhaps never will because she'll always be under pressure from the fact. Yeah, yeah. And she wants that Prada bag and the big diamond, you know. So, and quotas, whenever we feel that, you know, right now we have 25% reserved seats for women in politics and that's what one does. It rounds it up because there are general seats and then there are reserved seats and women have done a lot better in politics as well. So these avenues, but we don't have any quota system in the job market and the recognition in the job market. So if we are able to do that, I think that would be a big move ahead. That's an important point. Yeah, before you begin talking, I want to specifically take the point that was made earlier, security. Now an industry like yours, which sees a huge number of women employed, I think the BPOS have done a fantastic job for this country.  What they do in between is really none of our concern, but it has made them stay with you. Despite being married, despite, you know, doing night shifts, is that a model that other industries can replicate? Because we haven't seen a best practice like that being picked up. I mean, to your other point, of course. So I'll, you know, step back a little bit and say that first and foremost, we employ about a million people in India in the business. The company, Iran itself, has about 30,000 people. Okay? So we're used to large scale, but I must tell you, doing this is not easy.  It has to be driven.  By someone who really is committed to it. Yes, somebody has to be committed. You know, at the top level, you have to be committed. You have to. So in fact, I've made some notes here. We create targets and KRAs, you know, the board mandated KRAs, you know, for senior leaders. We actually look at, you know, sometimes we actually demand and drive a mandatory. Can you just say what KRAs are? Keer. Keer is our saviour. So we actually say, you know, this is one of your KRAs.  Because we spoke about education earlier. 1985, hardly five to eight percent of girls went into engineering in India. 2005, 40.4 percent of, you know, kids in the higher, you know, higher education are girls. So the ability to bring those people in is very high. But sensitizing people inside the company and enabling them, you know, to actually drive some of this is very important as well. So I don't want people to underestimate the difficulty. You spoke about the cabs. I actually think that is something we should not be doing. If we're saying empowerment, you know, and, you know, putting them on, you know, putting all of us on the same pedestal, why do we need to pick up and drop people? You know, why we do it? Because the government could not create the infrastructure, could not create buses, the bus system. So we do it. And therefore, when there is an issue, you know, when one of our employees gets into trouble or there is, you know, some kind of an issue in Delhi or any of the places, everyone says, oh, BPO company employee, this has happened, that has happened. The reality is I should not be providing that. The government should be, you know, doing that, okay? But let me tell you, some of the policies that we have, in fact, I have so many that I'll just read out a few. Some of the policies that we have inside the company, again, this is easily, you know, replicable, can be done across any industry, hiring from specific campuses. So we focus on campuses which are, you know, women-oriented, for example, one. Second thing, running campaigns to attract women, re-employment, after maternity, referral campaigns, and incentives for encouraging women, right? We actually pay, you know, leadership awards inside the company for people who do it. Beyond that, we also recognize that based on the phase of life of the woman, there is a special need again, right? You have to also, you know, think of that.  So that's the big opportunity.  That husband, for example, you know, the in-laws.  And the reality is all of this is available. The other thing we need to do and which we focus a lot on is this whole urban rural divide. If you ask me, our experience, like both of you said, on the rural side is far better, right? Far superior. So if you look at my Nasik facility, 50% of my workforce are women. The company average is 38, right? So, you know, they're waiting for these jobs. They're, you know, attrition is the lowest for me and my ability, therefore, to replicate this model more and more is extremely high.  So we spoke about leaders and, you know, the top layer, middle and, you know, the lowest. Obviously, in a company like ours and in our business, the lowest level is extremely well represented. It's always a challenge at the top and it has to be a topic of focus. We actually run initiatives to drive that. So every six months, a leadership team, you know, meeting takes place, 40 people, looking at the inverted L, you know, how it is represented, how the boxes are getting filled up, things like that. But a recent study actually, you know, this will surprise you, actually showed that 11% of the companies that they looked at in India actually were run by women now. In the US, it's 3%. So I think there's a big problem in the US as well. I think, you know, India has started making, you know, some kind of progress, even if it's at the highest levels. But recently, there was an article I read where, you know, the person actually wrote that following this gender, you know, kind of policy or pushing this model actually meant that some of the companies were not able to perform, you know, well, because they were, you know, paying too much of importance. I think this is completely, this is nonsense, completely uncalled for. And I don't see why, you know, the media would even print such an article, but it is done, right? I take the blame for it, but yeah, I'll let you take the question. No, actually, you know, it's so encouraging, actually. I think you should come and run some workshops in lots of different places. I actually think it's, you said some things which in some ways, I think are exactly what need to be said. And in some ways, I think they also really build on what Kiran pointed out a few, you know, a few minutes earlier, but which is to say is that you need a different set of strategies at every level of intervention. And when you're trying to change something that has been sort of, it's not just decades old, it's, we're talking about millennia, we're talking about millennia, and it's not just unique to one culture. I mean, this notion that women have a huge, big, less than sign, it's as distinctive as a Bindi if not, you know, more. We don't, you don't actually see it, but it's as though we carry a huge, big, less than sign in front of us in every culture that we walk around in. And so I think the notion that we're going to be able to change this overnight, no matter at what level you are at. And I think in some ways, you know, that that term necessity is the mother of invention makes complete sense, all right? When you're at the closest to survival stage, you know, why do lower class women actually have the courage and the gumption and the ability to just go out and do it? Well, it's a question of putting food on the table. For them and their kids. And they're not going to be able to make a compromise on that. It's survival and they're going to work, you know. So whether you tell them whether it's not what a girl, a woman should do, it's once you start getting into these sort of, you know, these, on the one hand, the middle class aspirations that Dilip mentioned are actually wonderful aspirations. You know, modernization is this sort of mixed bag, right? On the one hand, modernization enables you to imagine a different kind of a world. On the other hand, I think I would argue that modernization certainly in the context of traditional societies like ours, all across South Asia, has brought a different set of pressures. So dowry, for example, which used to be something like, you know, you stitched a beautiful shawl and you made some embroidery and you had a couple of barterns. As we began to see the opening up of the economy in India, I mean, my first participation in a dowry play was as a college student in Delhi University in 1979. And it was because dowry was beginning to be something completely connected to these aspirations. So now you needed a mixie, a TV, a scooter, a car, an air conditioner. So how do we think about these aspirations of consumption that are also driving a certain kind of devaluation of women or a sort of a limited commercialization almost of sort of the value of women? So I mean, I think we have to look at these things together. And I think the only way in which you begin to try and shift that is on the one hand, you have workplaces that are doing it in the way you were describing. And I do think you have to be more aggressive in sharing this with other industries. I don't think you can expect other industries are just going to come to you and say, hey, you know, tell us how it works because we'd love to do it. I think you have to be sort of an advocate. Also it's never easy for any other industry to pick up that model, but if you have a point. So the underpinning of all of this, and if you ask the question, why? The 20th century society has been very rigid, very hierarchical, very defined outcomes and roles. 21st century is getting less rigid. And the industry segments or the employment areas or the vocations that allow the person to choose the time and the period that they want to work for are finding greater acceptance. So, you know, and it's not gender specific. You know, it's very interesting. The biggest highest course in demand, you know, IT may not be the highest course in demand for women. The highest course in demand for women is the beautician's course. And because they can do it at their time and space in their area, et cetera. In the things of workforce, in the state of education, those states that have been able to adjust their education timings, surprise. Why doesn't a state like Madhya Pradesh have schools starting at 11.30? Normally it's seven o'clock in the morning, but they say, no, people want to go to the farm in the morning and want to go to the farm in the evening. So we'll have school from this time to this time. So then the enrollment rates went up. Access, give them bicycles. So you need to actually study and use this and build in flexibility, you know. I mean, the whole education system is you study when we want to, you give exams when you want to take them, and you go from one year until 11, we want to take them. And the kids are not. Why are more people going into open university? Why are more people going into net learning? I think the challenge here is that if you make society less rigid, then we get inclusion, much more inclusion. And we use the whole power of the media and connectivity to actually enable people to get that. Dilip, you're even seeing a lot of young men going into the whole business of beauty. No, I mean, quite honestly, it's been really striking to me walking to any beauty salon in India. So you have a Javed Habib and a Shana Zusin. Yeah. But lots of young men who feel like now this is a valid kind of an occupation. Dr. Jho. Okay, you can wash somebody's hair, you can give them a massage, you can, it's not, again, you're beginning to, and I would agree with you, I think this movement into a new form of an economy. Again, I think it is important to say here that both men and women need to have that space to be able to kind of articulate for themselves what it is they want to be able to do and to have more choices to be able to move in and out of the workforce in terms of kind of what we do. And without doubt, I think some of the world's best chefs and beauticians are actually women. Also in Pakistan, you know, the space, the new space that these young men and women have found is being fashion designers. So every, and it is, actually it's not the space that they have found for themselves, but it is an acceptable space. You know, I don't know how it goes over here because obviously India is much ahead in terms of the middle class and, you know, the workforce related issues. But over there, you know, there are acceptable professions and then there are obviously relating to the mobility issue. But this fashion designing is something that everybody is aspiring to do now and it's now like getting into serious like you can earn a lot of money. Artist, fashion designers, both men and women and also it's working out for the urban side. But again, you know, moving away from professionalism, but I want to pick up your point, which is a very valid point, that, you know, there is this certain push for everything to be like a shared reality, a global reality and all that in which we are losing diversity. One of the common things that we share across the border is the diversity. You know, within our provinces, within each district, you know, in Punjab, there would be so many different districts having very diverse kind of realities based on the profession, based on the accessibility and otherwise. So we have to, you know, it's painful work to recognize that and have to move things accordingly, but people and the rural areas will be functioning according to that. But for the policy and industry and, you know, even I was talking to teachers unions and they said that, you know, while developing a new curriculum, please come and talk to us at the district level. Some people are into fishing, some people are into agriculture, some people are into some other profession and they want that kind of training to go into that because in Pakistan, we don't have that many technical centers and women's technical centers. So I think for women, especially this diversity, you know, we need to now start pushing from, there are three levels obviously, but pushing it a little bit because it's inconvenient, but it needs to be pushed the diversity. Let me share with you a very interesting experience which I have been experimenting with great success by now. I set up a business school for the poor. You always hear a business school, presumably for the rich. This business school is called not business school for poor, I use the word business school for the marginalized. In this isn't beauty a business, right? Isn't animal husbandry even one cow a business? Even plowing your own field and vegetable selling a business? When I start to want it, and I call it the business school for the marginalized, we run it from Sona right here. And I have my first batch of 30 students. Who are those 30 students? Exactly what Mr. Shanoi said. If I had made it into nine to one, I would have not even had one student. But I made it 12 to two. I do it two hours a day. They finish the morning work. They milk whatever they've done. And the attendance is now 90% and above. What have they learned? It's a six month course which I've designed. In that, they're learning rural management. I'm saying when Dilip said, we may have to take a lot of women out of agriculture. I would say let's improve the skills of women in agriculture. And these business schools for if you would help partner work with, let us set up business schools for these women. How do they do better agriculture? Mushroom doesn't need much space. They've gone and visited Pusa Institute. How could they do mushroom cultivation? And they've gone to various exposure trips. And in this six month course, when I did the recent feedback, do you know one thing they earned each one got today? That day was confidence. Look, that's not available off the shelf. So I'm saying let's look at innovative, cost effective methods. I don't charge a fee. I charge even 100 rupees. Do you know what I did? I asked them, the fee for the school is 400 rupees for the whole batch. They didn't even want to pay 400. I said, okay, if you put in 400, I'm gonna give you back 500. But put 400 today, beg, borrow, steal. Because I don't want your money. I want your attendance. Because now that I have 400 rupees of theirs to be giving back 500 with skills, they're all attending to take the 400 back. But also in the process skills. I would say it's like a strategy for the bottom level. We need to find innovative, customized, time-flexy and skills-oriented where they're comfortable with program.  It's a three-inch program. I've started with hands, heart, and head. It's not head, heart, and hands. It's hands. Then I work with the hearts on value-based. And then I work on their knowledge skills. It's just working like a dream. So what I'm saying is, how do you do this though at the level that you talked about at the top? Because I think one of the things that is disturbing to me, I mean, this number, for example, I was recently exposed to in South Delhi, which is the most elite area of Delhi. You have the highest percentage of female fetus site. So the irony of progress, the irony of sort of, you know, having arrived, the 9% growth rate, the excellent income, the upper myth, you know, how do you shift mindsets when you have everything?  You're still reinforcing this idea that you can't inherit property. I mean, I think you're right. Both of you have asserted that sort of in some ways, at the very bottom, people are really willing to step forward. How do you change this mentality when you're at the level that you were talking about, you know, which is a very different level. People have, you need to talk about the pyramid. You need a different strategy for different level. You need to understand that. And I would think the middle level strategy where I thought we could, when we talk about strategies, most important is easy access to self-skilling. It's very, very important. But their education quality has to be about confidence-building, self-esteem, value for equal respect for gender. There are a lot of things. Now, these, you have to take, talk a different language for a different level. But don't you feel that the messages we're getting in society as a whole are kind of sending us a completely different message?  And Malika Sarabhai pointed out that, you know, what is the message that you get when girls are sexualized at an earlier and earlier age? When the sort of, you know, what we see are sort of, you know, quote-unquote bimbos on television. Where the level of gravitas that, you know, where even ministers in the Indian government are saying, well, you know, if girls wear jeans, they can't, they're basically asking to be raped. I mean, there is a kind of a overall mindset that we're seeing on the internet. You mentioned a point about, I'll just take it from there. You mentioned a point about how it's very aspirational because you're watching television today. What is television showing you?  It is just stereotype. None of those women work. They're all teched up all the time. They're all home. I mean, look, what is it? But, you know, fascinating. You must actually see the power of television. Right? Who do you think watches Masterchef? Right? Well, I forgot to. Okay, yeah. My son does. Now, if you look at the popularity of programs like that, right? They outweigh the popularity of, you know, in Gurdaspur, we did an analysis that, you know, we want to set up, you know, Punjab is the heart of engineering in the country. And, you know, we'll set up a lath or something like that. No, we don't want a lath.  You want to participate in Indian Idol and dance in your dance. So, you know, and the best part is that, you know, Kavitha, the point that you made, the top will never change. It'll be the middle and the bottom which will force the top to change, right? And the way it is happening in the middle today who are reaching the age of 20 in their ability, they're not born with any baggage. They are coming out fresh, right? And their percentage is 60%. They're far outnumber the larger things. And because they have been given access to this, you know, whatever education, whatever television, they will drive change. And they have to necessarily be a productive part of society. So, they will come for learning in agriculture. They will come to become businessmen because they know that without having those skills, they're not going to succeed. And that's what's going to happen. You know, for top down, either trickle down theory has worked, not top down change has worked. So, you know, you don't... I'll just have to cut you short there because I think there are some questions from the audience. I'm going to come back to you for final comments. Please raise your hands, identify yourselves and address your questions to a particular participant you want to, yes. Good afternoon, my name is Opasika. I'm a global shaper from the Chennai hub. My question is actually to the panel in general. Forgive me if this isn't the forum to discuss it, but it was gender parity that was the subject. We are talking about the men and the women and the third gender is completely ignored and nowhere during the forum that issue has been discussed. And I don't think it's a matter of prioritizing women over the third gender. So, how can we... You mean transgender individuals? Yes, the transgenders. So, how can we make it more inclusive and how can we provide them with the support system that's required to bring them up because as I see it, women are facing a problem with empowerment, but the transgenders are facing a worse problem. They're ostracized by society and they go through a lot of mental trauma because of their non-acceptance in society. Thank you. Would you like to take that, Rabita? Yeah, I mean, I don't know if you want to take a couple of questions and then we can respond. Yeah, we could. Yeah. There's someone right behind you. There's another question. I think you can't see. Hi, I'm Caroline Boudreau. I'm the CEO of the Miracle Foundation and I'm a young global leader. I have a question for you, Mr. Is it Margaisi? Yes, please. Yes. And it sounds like a superficial question, but it's really a very deep question and the question is why? Why are you doing such a great job of including all of these women? You know, what is your driver if there's really no compulsion from other people? Why are you doing this? Because they're just great, great employees. They're simple as that. They just, they work very well.  Frankly, we actually in our Philippines operations have a lot of them. We're learning from that experience to take it across our 10 other countries at this point in time. So I can't talk to you as an expert at this point in time because we are still studying that whole phenomenon. It's new to us. It's a one year old phenomenon to us, but the reality is that team is extremely comfortable in working in our business generally and at the company as well. And we now recognize in fact recently when I went for my UID card, I actually found you had three genders there, right? And that set me thinking in terms of how, you know, how we need to actually introduce this much faster than we have traditionally done. But the reality is, you know, we do it because it just makes great sense. It just makes business sense, I guess. It's not just business sense. It makes great sense in all aspects. Human sense, yes. Human sense, yes.  Yeah, I just wanted to mention that recently in Pakistan we have started to, like in the past two, three years, recognize the third gender and give out identity cards. Right, because before that, they were not even empowered to take identity cards.  But I think that then we thought about it and then we have left it as the third gender. You know, in Pakistan, these things, like I would say that for certain matters, India's far, far ahead in discussions of these matters and getting, but for Pakistan to have that in the law is great and so we decided that we will leave that in the law. You know, it says children and the third gender. You know, so we were saying that say girls and boys and the third gender because then when you do children, it's very dangerous also because then the girls are left behind, you know. So. Yeah, I just want to say that I think this whole question of gender, I mean, I've been very humbled for 14 years prior to coming to the Ford Foundation. I ran the Global Fund for Women and five years, sort of in 2005 or six, activists from the Balkans came to us and said, you call yourself the Global Fund for Women but does that mean you won't support grantees like us who identify as queer or as transgender? And it took us also a process like you were going through, you know, because the women's movement has mixed feelings about this. You know, it has fought so long and so hard from this platform of believing that women have been excluded, that it's kind of hard to kind of now come to terms with especially young people who are saying, why do we have to be put in a box? I mean, what was so interesting is that many of these young people, you might look at them and not necessarily think they were transgender. You might think that they were quote unquote straight. What they were saying is our humanity, our sexuality and our level of interaction and our ability to love people is on a continuum. And why do we have to be put into a box that says he, she, or it? We're human beings and we should be treated with the dignity and the rights that all human beings should have. I do think it requires an opening up of our own minds to be able, we've made steps in India around issues of gay and lesbian rights. Barkha Dutt just had a wonderful show on television day before yesterday or yesterday on talking to the parents of gay and lesbian young people. I think there is a new generation, both here in India as well as in different parts of the world.  This is difficult stuff to walk into and I think that the best we can do is to have people like yourself continue to raise it, have our own leadership in different institutions, whether it's NGOs like the Global Fund for Women or companies like the ones you run, be in a position where we're open and where we're listening and we're not sort of closing down out of fear. I'm being prompted. We've completely run out of time. My apologies to all of you. You will not get a chance to speak, but it has really been an engaging discussion, an hour passed by and I did not notice. So I guess these are relevant topics, very many takeaways. First, of course, like Kavita said on the panel, gender exists between your years and not what is between your legs. Ms. Bailey talking about the strategization, you talking about what corporate India can do. You essentially talking about education and of course making the whole point about skills and empowerment there. I do hope that the audience will go away with some of that food for thought. And the next time we meet, we will perhaps be talking about a gender gap that has been bridged. It's been a pleasure being with all of you. Thank you. Thank you. Yeah, hi. Just a second.


up until now we have been talking about phenomena of electrostatics. Electrostatics basically implies the effect of fields that is created by static electric charges. What we are going to do now is to talk about a different phenomena and that is the production and the properties of the magnetic field for which the source is a steady current that is a charge in motion. Basically there is one major difference between electrostatics and what we will be calling as the field of magnetostatics. We know that electric charges can be isolated namely I can have a single positive charge or a negative charge. However, it has never been possible to isolate a magnetic charge namely either a magnetic north pole or a south pole individually. Whenever a magnetic north pole is there accompanying it will be a magnetic south pole that is the net magnetic charge is always 0. Therefore, that is one of the major difference what we say is magnetic monopoles do not exist. However, I must tell you that there is really no theoretical reason why magnetic monopoles do not exist. However, in spite of several attempts to isolate such things it has not yet been possible. The source of a magnetic field is an electric current that is a steady current which is flowing let us say in a wire or on any other conducting loop. Now, in such a field the a moving electric charge experiences a side wise force. Remember that an electric field can exert a force on a charge whether it is moving or not. However, the magnetic field is characteristic in the sense that it only exerts force on a moving charge and this force which is given by the expression v cross b. So, if I have electric and magnetic field I have the net force is given by q which is the charge times the electric field which is the result of or of the electric field plus v cross b. Now, notice that this force due to the magnetic field is expressed as a cross product of the velocity with that magnetic field which means if the charges were static it will only experience an electric field, but in order that it experiences a force in a magnetic field the charge must be moving. This is known as the Lorentz force expression. So, what we have said is the current is the source of the magnetic field. Now, let us define current in a proper way current by itself is a scalar quantity. This is basically the amount of charge that is crossing the boundary of a surface s of a volume v. So, whatever is the amount of charge that is crossing an unit area per second per unit time that is what I call as the a current. So, in other words this is supposing I take a volume which is let us say defined by a boundary s the rate. So, if certain amount of charges flow into that volume the amount of charge in that volume will increase. Now, in steady magnetic phenomena or in a steady state phenomena I do not expect an accumulation of charge and this gives rise to what is known as the equation of continuity. Now, let us look at what is equation of continuity. Now, firstly let me assume that this is a volume and this s is a surface which separates two parts of that volume the volume to the left and the volume to the right. So, therefore, if electric charges are crossing this boundary the from the left I will expect a depletion of the amount of charge and of course, to the right there will be an increase in the amount of charge. Now, so therefore, what happens is this that this current that I have got which is there is a minus sign wrong here, but which is the dot product of a quantity which I call as the current density and this is the current density which is crossing a surface and it is that surface should be normal to the direction of the flow J dot d s. So, therefore, the rate of change of the charge in that volume which is d q by d t is given by well q is nothing but the charge density integrated over the volume. So, therefore, this quantity since this is the amount of charge that is increasing in the left part of the volume that must be the decrease from this side and which is nothing but the minus the J dot d s which is minus of the current. So, and I know that by using the divergence theorem I can rewrite this as del dot divergence of J over the volume. So, therefore, I have got d rho by d t d v integral is minus integral of del dot J d v and if I bring it to one side and use the fact that this is independent of what volume we take it is true for any volume what I get is this equation which is d rho by d t plus del dot of J is equal to 0. This is known as the equation of continuity basically it tells me talks about conservation of charge. So, if the left side of the volume is losing some charge because of the current flowing into through the surface. So, I must have that increasing a corresponding amount of charge on the right hand side. Since, we will be interested in primarily magnetostatics namely my currents are steady. So, therefore, I must have d rho by d t equal to 0 because there is no accumulation of charge in the volume and as a result the corresponding equation then becomes del dot of J equal to 0. So, this is the steady state form of the equation of continuity one point which of course will not be explaining in any detail is to tell you that this equation is also relativistically valid that is if you use what is known as Lorentz contraction then you will find this equation will transform co-variantly under it. So, this is just to tell you that the equation this equation is lot more rigorous and powerful than we thought it was while doing electrostatics we have been familiar with the basic law which is the Coulomb's law which essentially told you that the force between charges is given by an inverse square law namely q 1 q 2 divided by r square and there was a multiplicative constant dimensional constant 1 over 4 pi epsilon 0. Now, if I have had a charge distribution what I would do is that electric field due to this charge distribution at a point I build up by finding out what is the electric field due to a volume element containing the charge in that distribution at that point P where I am looking for the electric field. Now, since we have said that the source of magnetic field is a current distribution. So, what we do is we look at when we look at a circuit we look at individual current element that is a small length of the wire let us say carrying current and I define the direction of the length element along the direction in which the current happens to be flowing at a particular point on that circuit. Now, if this d l so I times d l is the length element regarded as a vector in the direction of the current. So, I times d l is my current element. Now, what we do is this that we calculate the magnetic field at a point P this picture illustrates this that this red thing is a current carrying wire and here I have shown a small section of it and this is the direction in which the current is being carried and I am interested in calculating the magnetic field due to this current carrying system at this point P. Now, similar to Coulomb's law we have a law here which is known as the Byte-Savart's law and Byte-Savart's law tells you that if you take a current element I d l the magnetic field d b due to that current element is given by a first like 1 over 4 pi epsilon 0 I have a constant here which I will come back to which is mu 0 by 4 pi. Now, current element since I is a scalar I will write it separately I d l. Now, the d l cross the position of the point where I am looking for the magnetic field with respect to the position of this d l. So, if you refer back to this picture again you find that if I am looking for the magnetic field at a point P which is with respect to my arbitrary origin at a vector position r and the current element is at a position r prime vector. So, with respect to that current element the point P is at r minus r prime. So, coming back to this formula again I have d l cross r minus r prime which is the vector distance from that current element and divided by the distance r minus r prime cube and you can see that this is also essentially an inverse square law because there is a power in the top and a power in the bottom. This constant mu 0 is known as the permeability of the vacuum or permeability of the free space. So, at this moment we will leave it at that that this is the constant which appears in the Biot-Cybert's law just as a constant 1 over 4 pi epsilon 0 with epsilon 0 being known as the permeability of the free space given. So, this has something to do with the magnetic properties of the material if there is a material then the mu 0 will change, but we will come back to it at a later stage. So, this is the Biot-Cybert's law. So, when you have a current carrying circuit and you are interested in finding out what is the magnetic field at that point at a particular point then you split your current distribution into a large number of infinitesimal current element and the Biot-Cybert's law gives you the magnetic field and at that point and essentially what you have to do is to sum it up namely integrate it. Now, what I will do is this that I will try to get a slightly different form of this Biot-Cybert's law by doing a little bit of algebra. So, let me let me look at what we are looking for. So, let us look at this.  Now, remember what I had, supposing I wanted instead to write it in the form of a current density. So, remember I had I times d l. So, I is a current and d l is of course, a length and I know that what I could do is to write this I as j dot d s, where j is the current density. So, therefore, that area element which goes with the current density to define my current and the length d l taken together gives me a volume. So, therefore, my magnetic field at the point p can be expressed as B let us say at the point r is given by mu 0 by 4 pi integral. Now, remember this r is a fixed position with respect to an arbitrary origin. This is the point at which I am determining the magnetic field. Now, this is not a quantity which is varying, but when I have quantities belonging to the source I am going to write it as given by r prime vector.  So, this is my magnetic field expression. Now, I am going to do a bit of a algebraic manipulation.  So, what I am going to do is this I am going to write this expression in a slightly different way. I will write it as a mu 0 by 4 pi. I have a minus sign if I write it as a gradient of 1 over r minus r prime. Now, in order to take care of that minus sign I am going to interchange the order of the cross product which is j of r prime d cube r. Now, so what I am going to do now is this I am going to rewrite this. So, I have got gradient 1 over r minus r prime cross j r prime. I will write it as equal to mu 0 by 4 pi integral del cross I will come back to the explanation of this of 1 over r minus r prime times j of r prime.  So, if I have a del cross of a scalar times a vector this is equivalent to this scalar times del cross of that vector which in this case is 0 because this gradient operator is with respect to variable r del which of course, we have said in this particular case is not varying. So, del cross of j r prime is 0. So, I have got del cross scalar times a vector is a scalar times del cross of vector which is 0 plus gradient of the scalar cross product with vector. So, this is the result that I have got. So, I have written it this way and this integrated with d cube r prime.  So, I will write this as mu 0 by 4 pi del cross of integral of j r prime divided by r minus r prime. Now, this is a rather important form in which the Bayer-Sawart law is expressed. So, this is expressed in terms of a current density distribution in principle. Now, since the magnetic field is written as a curl of a quantity and we know that divergence of a curl is always 0. So, this tells you the magnetic field at the point b is such that its divergence is equal to 0. So, that is del dot of b is equal to 0. So, the magnetic field is such that its divergence is equal to 0. Now, this is actually a consequence of the fact that there are no magnetic monopoles. How do I say that? Recall that in electrostatics the corresponding equation was del dot of e was equal to rho by epsilon 0 where rho was the charge density. So, as a result since in this case I do not have magnetic charges free magnetic charges my that is I do not have monopoles the magnetic field is such that its divergence is 0. Now, we have said several times that if you have a vector field a vector field is uniquely specified by specifying its divergence and curl. Actually, there is something else to be done that is specify also the normal component of the field at some surface, but let us leave it at that. So, basically what we are saying is that a vector field can have a divergence and it can have a different curl different vectors field can have same divergence, but different values of the curl. So, in order to specify it completely I am going to now calculate how much is the curl of the vector v. So, let us look at what is the curl. Now, curl of b now this expression now is what has been obtained written by me sometime back as the Byatt-Sawart's law of expression. So, I have got mu 0 by 4 pi del cross of del cross of this quantity. Now, we have several times seen that a del cross del cross of a vector field is given by gradient of the divergence of that field del of del dot of a minus del square a. So, my curl of b since b itself is written as a curl of something.  This looks like a rather horrible expression, but let us try to look at simplify this. So, first what I am going to do is this I am going to look at the first term that is del del of del dot of this quantity. Now, look at this first before I calculate the del let us look at what is this quantity here divergence j of r prime by r minus r prime. So, what I am doing first is this since I know that the quantity is inside the variable of integration is r prime and the gradient is through with respect to r I can simply take this del dot inside.  Now, so this is again divergence of a vector times a scalar, scalar is 1 over r minus r prime. So, the same way we write it as the vector dotted with gradient of 1 over r minus r prime that is because scalar times del dot of j prime j which is a function of r prime is 0. So, I write this and now what I do is this since the gradient acts on a function of r minus r prime I will use a minus sign and make that gradient a gradient prime meaning thereby that it acts on the variable r prime and not an r and that is as long as it is a function of r minus r prime I can do that by simply adding a minus sign. So, I got this now this quantity now everything here is with respect to the prime coordinate.  So, this is this is a simplification that we have achieved of the first term of that.  So, I can convert this using the divergence theorem to this quantity dotted with d s prime and as we have done several times I can take the surface to infinite distances and make this integral vanish. So, I will be left with simply this term and we have seen that we are dealing with steady state magnetic phenomena and I had talked earlier about the continuity relation and we had said that for the steady state phenomena del dot of j must be 0. So, therefore, this is also 0. So, therefore, from the expression that I had written down here of the curl of b the first term vanishes and I am simply left with the second term. So, let me look at what the second term is. So, I am left with curl of b is equal to mu 0 by 4 pi del square of j of r prime by r minus r prime d cube r prime. So, this is and there is a minus sign entrant. So, what I will do is this as we have done several times I will take the del square inside, but I know that del square acting on the variable r has no effect on this j of r prime. So, this will be written as minus mu 0 by 4 pi integral j of r prime times del square of 1 over r minus r prime. Several times we have pointed out that del square of 1 over r is minus 4 pi times a delta function of r. So, this quantity is minus 4 pi times delta function which is a 3 dimensional delta function. So, I write a delta cube of r minus r prime these are all modulus of vectors. Now, because of this delta function I can do this integration there is a minus sign here minus sign here 4 pi cancels out and I will be simply left with j r prime delta r minus r prime d cube r prime which is nothing, but j of r and 4 pi has cancel out I am left with a mu 0 j of r. So, therefore combining the two I have got divergence of b equal to 0 absence of magnetic monopoles and curl of b is equal to mu 0 j due to compare these expressions with the corresponding expression for the electrostatic field. Remember del dot of b equal to 0 I had del dot of e equal to rho over epsilon 0 that was my electrostatic Gauss's law. So, of course we have already understood that why this is 0 and not something del cross e electric field was a conservative field. So, therefore the del cross of that was equal to 0, but you notice that del cross of b is given by mu 0 times j. Let me do an integral formulations of this equation. So, del cross of b equal to mu 0 j now suppose I convert this by taking so this is my circuit and I define a surface and I say that look in that case if I define a surface then I can write down del cross b dot d s is same as j dot d s. So, this would be a surface through which the current is flowing that is surface perpendicular to the direction of the current. Now, since this is true for an arbitrary surface. So, let me write it here. So, I get integral of del cross b dot n d s is equal to mu 0 times j dot n d s that is true of an arbitrary surface that you could take and because of that I must have integral of b dot d l. Remember that I have used Stokes theorem here which converts the surface integral of a curl to line integral of the vector field itself and j dot n d s is my current. So, therefore, this is mu 0 times i and this is usually called the Ampere's law of magnetism. In an identical way del dot of b equal to 0 can be converted into integral b dot d s is equal to 0 in the same way as we had converted del dot of e equal to rho by epsilon 0 to integral e dot d s equal to q divided by epsilon 0. So, this is the Gauss's law of magnetism. We do next is to use the Byrd-Sawart's law and the Ampere's law illustrate a few problems. I would like to point out that the physical content of Ampere's law is no different from that of the Byrd-Sawart's law. However, frequently if I particularly in cases where I have symmetry because it is expressed as an integral b dot d l and if you want to use a definition like that to extract information about b then I need this integral b to be expressed as a functional form which will be possible only if I have substantial amount of symmetry. So, therefore, Ampere's law has limited validity because it cannot be always used, but the your Byrd-Sawart's law is fairly general. So, let me let me start by taking a long straight wire. So, a long straight wire like this. Now, I am interested in calculating what is the magnetic field at a distance let us say r from the wire. Now, purely by symmetry consideration I can imagine that the magnetic field will be the same at the same distance from the wire. In other words, it can only depend upon the distance r from the wire. So, if I take a circle of radius r with the center at the location of the wire then this magnitude of the magnetic field everywhere must be the same. The direction of the magnetic field is given by the standard right hand rule that is if you hold the wire with your finger pointing in the direction of the current. The direction in which your fingers curl that gives you the direction of the magnetic field. In other words, the direction of the magnetic field is azimuthal. So, it is depends upon 5. So, in that case what I can do is I can calculate what is the integral of b dot d l by taking a circle of radius r. Since, b is the azimuthal and the circle that I take is also in the same direction b dot d l is same as magnitude of b times magnitude of d l and then the integration since magnitude of b is the same and the integration over d l will be nothing but 2 pi times r and that must be equal to mu 0 times the current that is flowing through. In other words, the field b at a distance r from the wire is given by mu 0 i by 2 pi r that is its magnitude times of course, the unit vector in the direction of 5 that was easy because the problem has substantial symmetry. Now, what I am going to do is this. I am going to recalculate the same thing by taking a by using Bayes-Sawart's law. So, if I use Bayes-Sawart's law let us look at how does it work. So, let me define the x y z axis the same way there is my x axis there is my y axis and the z axis is out of the plane of the paper. Now, I will take the wire in the direction of x axis and the point at which I am interested in calculating the magnetic field to be at on the y axis remember that I can always do it because I have an infinite wire. So, whichever point I am interested in calculating the magnetic field I simply that and I use it for defining my axis. So, what I do is this is my point p and this I will take as my this is my origin. So, this is my vector r. So, if I take a current element at a vector position r prime then this is my vector r minus r prime.   So, it is nothing but I times d x. So, let me return back to that.  Now, notice I cross r prime is of course 0 because r prime is also along the x axis. So, I am left with I cross r and r is taken along the y axis. So, therefore, I cross r is along the z axis. So, the unit vector k unit vector k times r minus r prime magnitude sin of this angle times sin of this angle. What I do there now is this that I can write this as equal to I want to write it in terms of this fixed distance r. So, notice that I have got r minus r prime since this angle is theta I can write this distance in terms of r times tangent of theta minus pi by 2 which is equal to minus r cot theta. I use this that my d x then. So, this is my x is equal to this is x is equal to r tan of this angle. So, therefore, it is minus r cot theta.  So, therefore, my magnetic field which is along the direction k mu 0 i by 4 pi.   So, this one will go left with r minus r prime square which is r square cos x square theta and I have a sin theta there. So, I get it as sin theta divided by cos x square theta r square cos x square theta and of course, r cos x square theta d theta that is that is my d x there. Now, notice this thing that things cancel out there. I am left with simply an integration of sin theta from 0 to pi. So, I am left with simply integration of sin theta from 0 to pi which gives me minus cos theta and when I put the limit I get a factor of 2. So, therefore, I am left with again k mu 0 i divided by 2 pi r which is of course, was obtained in a much simpler way in from the Ampere's law. I will use another application now to calculate the magnetic field on the axis of a circular loop as a an expression which is used several times for calculating other things in particular the field inside a solenoid. .. So, let us refer to this picture here. So, I have taken my circle which is in red in the x y plane. So, this is x axis this is y axis and z axis is along the axis of the circle that is perpendicular to the plane of the circle passing through its center. So, remember that what I am going to do I need my to apply biots of art law. So, I first need an expression for d l remember that i d l cross r minus r prime. So, let us look at the vector relationship first. So, I will find it easy to show it just for the circle let me show it along the x axis and y axis suppose I have a circle here this is essentially recalling some vector algebra that we have done this is in the x y plane. Now, what I am going to do is this I am looking at an element at an angle theta here making an angle theta with the x axis and the direction of that vector is along the tangent at the point p. The magnitude of the vector because I am taking a small element there is a times d theta if I take the element to be at the position theta making an angle d theta. So, I have a vector along the tangent to the circle of magnitude a d theta. Now, how do I resolve it along the x and the y axis. So, notice that I can resolve it like this and that now. So, therefore, since this is the vector which is of magnitude a d theta the x component is minus a sin theta because this angle is theta. So, therefore, this angle is theta and hence this is 90 minus theta. So, therefore, my d l will be minus a d theta minus because the direction of that component is along the negative x direction sin theta times i and of course, a d theta cos theta because cos theta direction the direction of along the y axis is positive j. The point p this is of course, really not the point p, but the point let me call it p prime that is the position at which I have got the current element. Now, the vector r prime itself which is this vector I can resolve it and that simply gives me a cos theta times i because this is in this direction it is outward direction. So, r prime vector itself is a cos theta times i plus a sin theta times j and the vector r returning to the slide the vector r is along the z axis I have rewritten the two relationship that we have proved. So, vector r is z times k. So, therefore and further the magnitude of r minus r prime by Pythagoras theorem is r square plus a square square root. Now, you put all of them in what is d l cross r minus r prime now. So, that is very easily calculated because r minus r prime r prime I have written now r is along the z direction.  So, if I divide this by distance which is a square plus z square if there was a cube there. So, a square plus z square to the power 3 by 2 d theta all these quantities are constant other than theta. So, therefore the integral of cos theta or integral of sin theta they give me 0 and I am simply left with a term which is dependent upon k. So, this gives me mu 0 i a square by 2 a square plus z square to the power 3 by 2 k I would like to point out that the current times pi a square which is the area of the loop is equal is defined to be the magnetic moment of the current loop. So, therefore this is also written as mu 0 by 2 pi m by a square plus z square to the power 3 by 2 if you take z to be very large then you notice that this gives me a 1 over r cube dependence of the magnetic field. We will see that this is nothing, but the way that dipole fields behave.


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