Two charges q₁ and q₂ are separated by a distance of 30cm. A third… | MHT CET 2026 (16 Apr, Shift 2)

Q11MHT CET 2026 · 16 APR · SHIFT 2Medium

Electrostatic Potential Energy

Two charges $q_1$ and $q_2$ are separated by a distance of 30cm. A third charge $q_3$ initially at point C is shown in figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of $q_3$ from C to D is $q_3k/4\pi\varepsilon_0$ , the value of K is ( $\varepsilon_0$ = permittivity of free space)

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Answer: (a)

$q_3$ stays 40 cm from $q_1$ , so only the $q_2$ term changes.
$BC = \sqrt{40^2 + 30^2} = 50$ cm $= 0.5$ m; $BD = 40 - 30 = 10$ cm $= 0.1$ m.
$\Delta U = \dfrac{q_2q_3}{4\pi\varepsilon_0}\left(\dfrac{1}{0.1} - \dfrac{1}{0.5}\right) = \dfrac{q_3(8q_2)}{4\pi\varepsilon_0}$
So $k = 8q_2$ , answer (a).

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