Question

What is the electric potential at the centre of a hemisphere of radius R and having surface charge density $\sigma$?

• A. $\frac{\sigma }{2{\epsilon }_0}$
• B. $\frac{\sigma }{{\epsilon }_0}$
• C. $\frac{\sigma }{{\epsilon }_0}R$
• D. $\frac{\sigma }{2{\epsilon }_0}R$

Answer 1

Answer: (D)

$\frac{\sigma }{2{\epsilon }_0}R$

The potential at the centre of a spherical shell can be written as the sum of potential due to two identical hemispheres
$V_{total}=V_{hemispher{e}_1}+V_{hemispher{e}_2}$
$⟹V_{total}=2V_{hemisphere}$
$⟹\frac{\sigma }{{ϵ}_0}R=2V_{hemisphere}$
$⟹V_{hemisphere}=\frac{\sigma }{2{ϵ}_0}R$