Question

A charge $+q$ is carried from a point $A\left(r,135^{\circ }\right)$ to point $B$ $\left(r,45^{\circ }\right)$ following a path which is a quadrant of circle of radius $r$. If the dipole moment is $p$, the work done by the external agent is (assume short dipole)

• A. 0
• B. $\frac{1}{4\pi {\epsilon }_0}\frac{qp}{r^2}$
• C. $\frac{1}{4\pi {\epsilon }_0}\frac{\sqrt{2}qp}{r^2}$
• D. $\frac{1}{4\pi {\epsilon }_0}\frac{qp}{r}$

Answer 1

Answer: (C)

$V_A=\frac{kp\cos 135^{\circ }}{r^2}$,
$V_B=\frac{kp\cos 45^{\circ }}{r^2}$
Work done $=q\left(V_B-V_A\right)$
$=\frac{1}{4\pi {\epsilon }_0}\frac{\sqrt{2}pq}{r^2}$