Question

A hemisphere of radius r is charged uniformly with surface charge density sigma, what will be the potential at the centre?

Answer 1

Given details:

Radius of the hemisphere is 'r'.

Surface charge density is 'σ'

Solution:

In the hemisphere, let us consider a small element of angle θ.

Potential due this small element will be dV = σ r / 2 ε * (sin θ dθ)

Now, let us integrate dV with respect to θ in the interval 0 to π/2,

So, at the centre of the hemisphere, potential will be given by V = σ r / 2 ε

Hope it helps. Thank You!