The magnitude of the electric field on the surface of a sphere of radius r having a uniform surface charge density $\sigma$ is

Given Data: A sphere of radius r and uniform surface charge density $\sigma$

Concept Used: Gauss Law of Electrostatics.

Detailed Solution:

We know, by Gauss law,

$\int E·dA=\frac{q_{\text{in }}}{{\epsilon }_0}$

Here, A- cross section area and qin- charge uniformly distributed inside the sphere.

We know, $\sigma =\frac{q_{\text{in }}}{A}$

So we have, $E.A=\frac{q_{\text{in }}}{{\epsilon }_0}$

$E=\frac{\left(\frac{q_{\text{in }}}{A}\right)}{{\epsilon }_0}$

$E=\frac{\sigma }{{\epsilon }_0}$