A magnet of total magnetic moment 10⁻² A m² is placed in a time varying magnetic field B = B₀ cos(ωt) where B₀ = 1 Tesla and ω = 0.125 rad/s. The work done for reversing the direction of the magnetic moment at t = 1 second, is__?

Correct option is C. 0.0198 J
Given:
M = 10⁻² î A m²
B = B₀ î cos(ωt)
B₀ = 1 T
ω = 0.125 rad/s
To find: work done for reversing direction of magnetic moment at t = 1 second
Solution: Let required work done be W. As we know that,
W = -||M|| * ||B|| (cos θ₂ - cos θ₁)
(now, θ₂ = 180°, θ₁ = 0°, ||M|| = 10⁻²)
W = -||M|| * ||B|| (cos(180°) - cos(0°))
W = -10⁻² * 1 * cos(0.125) * (cos(180°) - cos(0°))
W = 10⁻² * 1 * cos(0.125) * (-1 -1)
W = 2 * 10⁻² * cos(0.125)
W ≈ 2 * 10⁻² * 0.992
W ≈ 0.0198 J
Hence, the correct option is C. 0.0198 J