A 2 amp current is flowing through two different small circular copper coils having radii in ratio 1

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Question

A 2 amp current is flowing through two different small circular copper coils having radii in ratio 1:2. The ratio of their respective magnetic moments will be:

Accepted Answer

Correct Answer: B — 1:4Step-by-step Solution:Magnetic moment of a current-carrying circular loop: M = NIAFor a single circular loop: A = πr²So: M = I × πr²Since current I is the same for both coils: M ∝ r²Given r₁ : r₂ = 1 : 2:M₁/M₂ = r₁²/r₂² = 1²/2² = 1/4M₁ : M₂ = 1 : 4Why Option A (4:1) is wrong: This is the reciprocal of the correct answer. M ∝ r² (area), not ∝ 1/r². A common inversion error.Why Option C (1:2) is wrong: This would be correct only if M ∝ r (linear), but magnetic moment depends on area (πr²), not radius directly.Why Option D (2:1) is wrong: This gives r₂:r₁ ratio (reversed) and also incorrectly assumes M ∝ r.Key Concepts from Magnetism and Matter (NCERT Class 12, Chapter 5):Magnetic moment of a current loop: M = NIA, directed perpendicular to the plane of the loop (right-hand thumb rule).A current loop behaves like a magnetic dipole, analogous to an electric dipole.Torque on a magnetic dipole in a uniform field: τ = MB sinθ = M × B. Equilibrium at θ = 0° (stable) and θ = 180° (unstable).Potential energy of a magnetic dipole: U = −MB cosθ = −M·B.Gyromagnetic ratio of an electron: Ml/L = e/(2me).

A 2 amp current is flowing through two different small circular copper coils having radii in ratio 1:2. The ratio of their respective magnetic moments will be:

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A 2 amp current is flowing through two different small circular copper coils having radii in ratio 1:2. The ratio of their respective magnetic moments will be:

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