Two charges q1 and q2 are placed 30 cm apart, as shown in the figure… | NEET 2005 (AIPMT)

Q60NEET 2005 · AIPMTMedium

Electrostatic Potential Energy

Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D.

The change in the potential energy of the system is $\frac{q_3}{4\pi\varepsilon_0}k$ where k is

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Answer: (c)

$q_3$ stays $40$ cm from $q_1$ (it moves on a circle centred at A), so only the $q_2q_3$ term changes.
At C: $BC = \sqrt{30^2 + 40^2} = 50$ cm. At D: $BD = 40 - 30 = 10$ cm.
$\Delta U = \frac{q_2q_3}{4\pi\varepsilon_0}\left(\frac{1}{0.1} - \frac{1}{0.5}\right) = \frac{q_3}{4\pi\varepsilon_0}(8q_2)$
So $k = 8q_2$ , answer (c).

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