JEE PYQ: Electrostatics Question 43
Question 43 - 2019 (09 Apr Shift 2)
A system of three charges are placed as shown in the figure:
$+q$ at $x = 0$, $-q$ at $x = d$, and $Q$ at $x = D$ ($D \gg d$).
If $D \gg d$, the potential energy of the system is best given by:
(1) $\frac{1}{4\pi\varepsilon_0}\left[\frac{-q^2}{d} - \frac{qQd}{2D^2}\right]$
(2) $\frac{1}{4\pi\varepsilon_0}\left[\frac{-q^2}{d} + \frac{2qQd}{D^2}\right]$
(3) $\frac{1}{4\pi\varepsilon_0}\left[\frac{q^2}{d} + \frac{qQd}{D^2}\right]$
(4) $\frac{1}{4\pi\varepsilon_0}\left[\frac{-q^2}{d} + \frac{qQd}{D^2}\right]$
Show Answer
Answer: (4)
Solution
$U = \frac{1}{4\pi\varepsilon_0}\left[\frac{q(-q)}{d} + \frac{qQ}{D} + \frac{(-q)Q}{D-d}\right]$. For $D \gg d$: $\frac{1}{D-d} \approx \frac{1}{D}\left(1 + \frac{d}{D}\right)$. $U \approx \frac{1}{4\pi\varepsilon_0}\left[\frac{-q^2}{d} + \frac{qQd}{D^2}\right]$.
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