A closely wound circular coil of 100 turns and radius 5 cm produces a magnetic field of 3.14 × 10⁻³ T at its centre. Find the current in the coil and its magnetic moment. Take μ₀ = 4π × 10⁻⁷ T·m·A⁻¹.
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Question

A closely wound circular coil of 100 turns and radius 5 cm produces a magnetic field of 3.14 × 10⁻³ T at its centre. Find the current in the coil and its magnetic moment. Take μ₀ = 4π × 10⁻⁷ T·m·A⁻¹.

Options

G1 Physics · Accepted Answer

Step 1: For a closely wound N-turn circular coil, magnetic field at centre B = μ₀NI/(2R). Step 2: Solve for I = 2RB/(μ₀N). Step 3: With R = 0.05 m, N = 100, B = 3.14 × 10⁻³ T, μ₀ = 4π × 10⁻⁷, current I = (2 × 0.05 × 3.14 × 10⁻³)/(4π × 10⁻⁷ × 100) = 2.50 A. Step 4: Magnetic dipole moment M = NIA = NIπR². Step 5: M = 100 × 2.5 × π × (0.05)² ≈ 1.96 A·m² ≈ 2 A·m². Final answer: 2.5 A and approximately 2 A·m² (Option C).