Answer to Question #104212 in Calculus for Akshay

Question

Derive the expression for electric potential due a uniformly charged spherical
shell at a point outside the shell.

Answer 1

Let, R be the radius of the shell and Q be the charge uniformly distributed on the surface.

i) For a point outside the shell :

By Gauss's law, $E.4πr ^ 2 = ​ Q _{ en}/\epsilon_0 ​$

here r be the distance from centre of shell (r>R) and charge enclosed by surface $Qeq ​=Q.$

So, the electic field outside the shell is  $E = ​ Q _{ en}/(4πr^2\epsilon_0)$ , the electric potential outside the shell is $V(r)=-\int_{\infin}^r \frac{Q_{en}}{4\pi r_1^2 \epsilon_0}d r_1=\frac{Q_{en}}{4\pi r\epsilon_0}.$