Answer to Question #132014 in Electricity and Magnetism for Rohan

Question

A charge q is uniformly distributed on the surface of a cube and there is no other charge in consideration. Divergence of electric field is-

(a) zero inside the cube
(b) zero outside the cube
(c) zero on the surface of the cube
(d) zero nowhere.

Answer 1

We know that divergence electric field at any point is $\bigtriangledown.E=\dfrac{\rho}{\epsilon_o}$

If the cube made of conducting material then charge inside the cube will reflect over the surface of the cube so net charge inside the conducting cube will be zero hence the value of divergence of the electric field will be zero.

Now if cube is made of non-conducting material,

then electric flux $(\phi) =\dfrac{q}{\epsilon_o}$

But cube is made of six faces, and each have the same area, so flux through each face $=\dfrac{q}{6\epsilon_o}$

and divergence $\bigtriangledown.E=\dfrac{\rho}{6\epsilon_o}$

Hence correct answer is option A.