Two single-turn circular copper coils carry the same current of 2 A. Their radii are in the ratio r₁: r₂ = 1:2. Find the ratio of their magnetic dipole moments M₁: M₂.
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Question

Two single-turn circular copper coils carry the same current of 2 A. Their radii are in the ratio r₁:r₂ = 1:2. Find the ratio of their magnetic dipole moments M₁:M₂.

G1 Physics · Accepted Answer

Step 1: Magnetic dipole moment of a current loop is M = NIA. Here N = 1 and A = πr². Step 2: Both coils carry the same current, hence M ∝ r². Step 3: M₁/M₂ = (r₁/r₂)² = (1/2)² = 1/4. Final answer: M₁:M₂ = 1:4, Option A.