Question

A conducting sphere of radius $r=20cm$ is given a charge $Q=16\mu C.$ What is the electric field $E$ at its center?

Answer 1

Gaussian surface:

1. The charge given is uniformly distributed on the sphere due to which electric potential inside the sphere is constant.
2. The consequence is that the electric field inside is zero.
3. We can verify this in another way i.e., by Gauss law.
4. Gauss law states that for a gaussian surface, electric flux is equal to the ratio of charge inside and permittivity constant.
5. According to gauss law, ${\varphi }_E=\frac{Q}{{\epsilon }_0}$. Here, ${\varphi }_E=$electric flux through a closed surface $S$ enclosing any volume $V$, $Q=$total charge enclosed within $V$ and ${\epsilon }_0=$electric constant.
6. Electrix flux is equal to the product of the electric field and the area of the gaussian surface. Since $Q$ inside is zero. So, electric flux is zero.
7. Since the area of the gaussian surface that we drew is not zero, the electric field inside the sphere has to be zero.

Hence, the electric field in the center of the sphere is zero.