Why is the electric field inside a conducting hollow/filled sphere zero?

[aryan kumar pandey]

Homework Statement

a electric charge emits electric field lines radially. A charged conducting hollow/filled spheres have ellectric charges on its surface. How is the electric field inside the hollow/filled sphere zero?

Relevant Equations

E = kq/r^2

 

[Orodruin]

Start with the filled conducting solid. The stationary electric field inside any such conductor is zero because if it wasn't then that non-zero field would drive an electric current according to $\vec J = \sigma \vec E$, where $\sigma$ is the conductance. In particular, this means that any charge on the conducting filled sphere is located on the surface because according to Gauss' law $\rho \propto \nabla \cdot \vec E = 0$ inside the conductor.

Now we know that any charge on the conducting filled sphere will arrange itself on the surface such that the internal field is zero. This charge configuration is also possible on the hollow sphere and will be the lowest energy configuration also in that case. Hence, also on the hollow sphere, the charge configuration on the surface will be such that the field inside is zero.

 

[BvU]

Hello and !

This picture is not correct if you mean that the electric field lines start at the center. They start at the positive charges. The positive charges evenly distribute themselves on the outside surface of the conducting spherical shell: if they were not evenly distributed, there would be a potential difference and the charges would move until there was no potential difference any more.

Inside the spherical shell the electric field contributions from the charges on the surface cancel. It would be a good exercise to actually do the integral and see this happen.

The conducting shell is an equipotential surface where the electric potential is constant; the electric field is the derivative and therefore it is zero.

See here

If you have already learned about Gauss' theorem the math becomes easier.

$\$