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JEE Main 2022 (29 Jul, Shift 2) · Parallel Plate Capacitor

Parallel Plate Capacitor question from JEE Main 2022 (29 Jul, Shift 2)

Q10JEE Main 2022 · 29 JUL · SHIFT 2Medium

Parallel Plate Capacitor

Two identical thin metal plates have charges $q_1$ and $q_2$ respectively such that $q_1 > q_2$ . The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is:

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Answer: (c)

Charge on outer faces $= \frac{q_1 + q_2}{2}$ each; inner faces carry $\pm\frac{q_1 - q_2}{2}$ .
Only the inner charges make the field between the plates, so effective charge $Q = \frac{q_1 - q_2}{2}$ .
$V = \frac{Q}{C} = \frac{q_1 - q_2}{2C}$
So the answer is (c) $\frac{q_1 - q_2}{2C}$ .

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