Question

Charges $+q$ and $-q$ are placed at $A$ and $B$ , respectively, which are at a distance $2L$ apart. If $C$ is the midpoint between $A$ and $B$ , then work done in moving charge $Q$ from $C$ to $D$ (through semicircular path $CRD$ ) and from $C$ to $\in fty$ are, respectively,

• A. $\frac{q Q}{2 \pi \epsilon _{0} L}$ and infinity
• B. $\frac{q Q}{6 \pi \epsilon _{0} L}$ and zero
• C. zero, zero
• D. $\frac{- q Q}{6 \pi \epsilon _{0} L}$ and zero

Answer 1

Answer: (D)

$W_{C R D}=Q\left(V_{D} - V_{C}\right)$
$W_{C R D}=Q\left[V_{D} - 0\right]$ ( $\because $ potential at centre of dipole is zero)
$W_{C R D}=\left[\frac{k q}{3 L} - \frac{k q}{L}\right]Q$
$W_{C R D}=-\frac{k q Q}{L}\times \frac{2}{3}=-\frac{q Q}{6 \pi \epsilon _{0} L}$