Question

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

Answer 1

Gauss Law:

Gauss law states that electric flux through any closed surface is equal to the net charge enclosed inside the surface divided by the permittivity of vacuum.

Electric field due to a uniformly charged thin shell:

In the diagram, O is the centre of the spherical shell of radius R, and charge enclosed by the spherical shell is q.

Let a point A is outside the spherical shell, where we have to calculate the electric field.The distance between the centre of spherical shell and the point A.

ϕ=E.Scosθ

So, ϕ=E.4πr

2

−−−−−−−−−−−−−−(1)

As per gauss law,

ϕ=

ϵ

o

q

−−−−−−−−−(2)

From equation (1) and (2)

E.4πr

2

=

ϵ

o

q

Now,

E=

4πϵ

o

r

2

q

This is the electric field at the distance r, outside from the shell.