Electrostatic Potential and Capacitance - Result Question 15
17. Charges $+q$ and $-q$ are placed at points $A$ and $B$ respectively which are a distance $2 L$ apart, $C$ is the midpoint between $A$ and $B$. The work done in moving a charge $+Q$ along the semicircle $C R D$ is
[2007]
(a) $\frac{q Q}{2 \pi \varepsilon_0 L}$
(b) $\frac{q Q}{6 \pi \varepsilon_0 L}$
(c) $-\frac{q Q}{6 \pi \varepsilon_0 L}$
(d) $\frac{q Q}{4 \pi \varepsilon_0 L}$
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Answer:
Correct Answer: 17. (c)
Solution:
- (c)
Potential at $C=V_C=0$
Potential at $D=V_D$
$=k(\frac{-q}{L})+\frac{k q}{3 L}=-\frac{2}{3} \frac{k q}{L}$
Potential difference
$V_D-V_C=\frac{-2}{3} \frac{k q}{L}=\frac{1}{4 \pi \epsilon_0}(-\frac{2}{3} \cdot \frac{q}{L})$
$\Rightarrow$ Work done $=Q(V_D-V_C)$
$=-\frac{2}{3} \times \frac{1}{4 \pi \varepsilon_0} \frac{q Q}{L}=\frac{-q Q}{6 \pi \varepsilon_0 L}$
