Question: Q. 9. In the given figure, charge $+Q$ is placed at the centre of a dotted circle. Work done in taking another charge $f q$ from $A$ to $B$ is $W_{1}$ and from $B$ to $C$ is $W_{2}$. Which one of the following is correct?
(i) $W_{1}>W_{2}$
(ii) $W_{1}=W_{2}$
(iii) $W_{1}<W_{2}$
U] [CBSE SQP 2017-18]
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Solution:
Ans. (ii)
As $V_{A}-V_{B}=V_{B}-V_{C}$ magnitude of work done is same.
[CBSE Marking Scheme 2017] 1
Detailed Answer :
As we know $E=-\frac{d V}{d r}$ and inside a ring there is zero electric field which means constant potential
$\therefore \quad V_{A}-V_{B}=V_{B}-V_{C}$
$\therefore$ Magnitude of work done is same.
1
Answering Tip
- Points $A$ and $B$ are at same potential lies on a equipotential surface.
[I] Q. 10. What is the amount of work done in moving a point charge around a circular arc of radius $r$ at the center where another point charge is located? $\quad$ A&E [O.D. Comptt. I, II, III 2014]
Ans. Let $q_{1}$ be the charge inside the circle and $q_{2}$ be the charge moving around the circular arc, then work done
$$ W=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q_{1} q_{2}}{r^{2}} $$
The work done in moving the charge over the circular arc is zero, because it is moving over an equipotential surface.
