A ballistic galvanometer shows a first swing of 25° when a charge of 100 μC passes through it. What charge is required for a first swing of 50° (assume proportionality of first swing to total charge)?

Introduction / Context:
A ballistic galvanometer is designed to measure total charge passed in a short pulse. Its initial deflection (first swing) is proportional to the impulse of current and hence to the total charge, provided damping is small and the pulse duration is short compared with the galvanometer period. This is a standard proportional-scaling question.

Given Data / Assumptions:

• First swing θ ∝ Q (total charge).
• Case 1: Q1 = 100 μC → θ1 = 25°.
• Case 2: Q2 → θ2 = 50°.
• Same instrument settings and conditions; damping unchanged.

Concept / Approach:
Since θ ∝ Q, the ratio of deflections equals the ratio of charges. Doubling the first swing from 25° to 50° requires doubling the charge through the galvanometer.

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