The magnetic moment and moment of inertia of a magnetic needle shown are respectively 1.0 × 10⁻² A·m² and (10⁻⁶/π²) kg·m². If it completes 10 oscillations in 10 s, the magnitude of magnetic field is: [Image]
Options

Question

The magnetic moment and moment of inertia of a magnetic needle shown are respectively 1.0 × 10⁻² A·m² and (10⁻⁶/π²) kg·m². If it completes 10 oscillations in 10 s, the magnitude of magnetic field is: [Image]

Options

G1 Physics · Accepted Answer

Step 1: Oscillation period T = 10 s/10 = 1 s. Step 2: T = 2π√(I/(mB)). Hence B = 4π²I/(mT²). Step 3: Substitute I = 10⁻⁶/π² and m = 10⁻²: B = [4π² × (10⁻⁶/π²)]/(10⁻² × 1²) = 4 × 10⁻⁴ T = 0.4 mT (option C). Final answer: (C) 0.4 mT.