To show that this quantity is unique for a given physical system, one shows that the difference between two distinct solutions for it would have a gradient whose square would have volume integral zero.
To show that this quantity is unique for a given physical system, one shows that the difference between two distinct solutions for it would have a gradient whose square would have volume integral zero. This quantity is set equal to zero in the incomplete Weyl gauge. It may be written as a sum of solid harmonics times multipole moments in the Laplace expansion. This quantity's Laplacian equals charge-density over permittivity, according to Poisson's equation. This quantity is constant everywhere along a conducting surface. By integrating Coulomb's Law, one finds that this quantity for a point charge equals kQ over R. For 10 points, identify this electrostatic quantity, whose negative gradient is the electric field, and which has units of Joules per Coulomb.
To show that this quantity is unique for a given physical system, one shows that the difference between two distinct solutions for it would have a gradient whose square would have volume integral zero.
electric potential [or scalar potential, or voltage, prompt on "phi" or "V", do not accept "potential energy"]