Question

A charge of $10\mu C$ is distributed uniformly over the circumference of a ring of radius $3\text{m}$ placed on the $x-y$ plane with the axis at origin. Find electric potential at point $P(0,0,4\text{m})$

• A. $1.8\times {10}^6\text{V}$
• B. $18\times {10}^4\text{V}$
• C. $18\times {10}^3\text{V}$
• D. $1.8\times {10}^2\text{V}$

Answer 1

The correct option is C $18\times {10}^3\text{V}$

Given that,
Radius of the ring, $R=3\text{m}$
Distance of point $P$ from the axis of ring, $z=4\text{m}$

The electric potential of uniformly charged ring of radius $R$ at axial distance $z$ from the ring is given by
$V_P=\frac{kQ}{\sqrt{z^2+R^2}}$
$\Rightarrow V_P=\frac{9\times {10}^9\times 10\times {10}^{-6}}{\sqrt{4^2+3^2}}$
$\Rightarrow V_P=18\times {10}^3\text{V}.$

$\begin{array}{c}\text{Why this question ?}\\ \text{Concept: This question helps in the}\\ \text{visualization of orientation of ring}\\ \text{and corresponding point.}\end{array}$