Question

A thin ring of radius $R$ metres is placed in $x-y$ plane such that its centre lies on origin. The half ring in region $x<0$ carries uniform linear charge density $+\lambda \text{C/m}$ and the remaining half ring in region $x>0$ carries uniform linear charge density $-\lambda \text{C/m}$. Then the electric potential $($in $\text{volts})$ at point $\text{P}$ whose coordinates are $(0\text{m},+R/2\text{m})$ is

• A. $\frac{1}{4\pi {ϵ}_0}\frac{\lambda }{2}$
• B. Zero
• C. $\frac{1}{4\pi {ϵ}_0}\frac{\lambda }{4}$
• D. Cannot be determined

Answer 1

The correct option is B Zero

Consider two infinitesimally small elements on ring having charges $+dq$ and $-dq$ symmetrically located about $y-$axis as shown in figure.



Potential due to this pair at any point on $y-$ axis is zero.

The sum of potentials due to all such possible pairs is zero at all points on $y-$ axis. Hence potential at $\text{P}(0,\frac{R}{2})$ is zero.

Hence, option (b) is correct answer.