Question

Find the electric potential energy of a uniformly charged sphere.

Answer 1

The electric potential Energy of uniformly charged sphere is

$\frac{3q^2}{20\pi \epsilon_0 R^2}$  .

Charge density of sphere= $\frac{Q}{ Volume of sphere}$

Answer 2

We have an uniformly charged sphere.

•) Now we have to find the electric potential energy due to this uniformly charged sphere .

•) Now let , 'Q' be the total charge of the sphere , 'a' be the radius of the sphere and 'r' be the distance between the change q at a point 'P' and the sphere .

•) Now , let W be the work and F be the electrostatic force.

W = § F.dx where limits of integration is from infinity to a

•) Now we know that ,

F = E*dq , where E is the electric field and E = kq / r^2

=> W = § kq*dq / a

=> W = kQ^2 / 2a

Where, k = 1 / 4π€