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. $\frac{1}{4 \pi \varepsilon_{0}} \frac{q p}{r^{2}}$
• C. $\frac{1}{4 \pi \varepsilon_{0}} \frac{\sqrt{2} q p}{r^{2}}$
• D. $\frac{1}{4 \pi \varepsilon_{0}} \frac{q p}{r}$

Answer 1

Answer: (C)

$V_{A}=\frac{k p \cos 135^{\circ}}{r^{2}}$,
$V_{B}=\frac{k p \cos 45^{\circ}}{r^{2}}$
Work done $=q\left(V_{B}-V_{A}\right)$
$=\frac{1}{4 \pi \varepsilon_{0}} \frac{\sqrt{2} p q}{r^{2}}$