Question

The diagram shows a part of disc of radius $R$ carrying uniformly distributed charge of density $\sigma$. Electric potential at the centre $O$ of parent disc is

• A. $\frac{\sigma R}{2{ϵ}_0}$
• B. $\frac{\sigma R}{16{ϵ}_0}$
• C. $\frac{\sigma R}{24{ϵ}_0}$
• D. $\frac{\sigma R}{32{ϵ}_0}$

Answer 1

The correct option is B $\frac{\sigma R}{16{ϵ}_0}$


Potential $V_o$ due to the entire disc is $V_o=\frac{\sigma R}{2{ϵ}_o}$
Since potential is a scalar, potential due to quarter of a disc at $O$. i.e.
$V_1=V_2=V_3=V_4=\frac{\sigma R}{8{ϵ}_o}$


In the above diagram
Potential at $O$ is $V_o=V_R$ (Potential due to quarter disc of radius $R$) $-V_{\frac{R}{2}}$ (Potential due to quarter disc of radius $\frac{R}{2}$)
$V_o=\frac{\sigma R}{8{ϵ}_0}-\frac{\sigma \left(\frac{R}{2}\right)}{8{ϵ}_0}=\frac{\sigma R}{16{ϵ}_0}$