Question Detail
Question
A coil has 45 turns and an area of 1.8 x 10-2 m². If the torque on the coil is 2.5 x 10-2 Nm when placed in a magnetic field of 0.08T, calculate the current flowing in the coil.
Correct Answer
Option B is the correct answer.
Detailed Explanation
The maximum torque (τ) experienced by a current-carrying coil in a magnetic field is given by τ = N I A B, where N is the number of turns, I is the current, A is the area, and B is the magnetic field strength (assuming the magnetic field is perpendicular to the magnetic moment of the coil, i.e., parallel to the plane of the coil for maximum torque). Given: τ = 2.5 x 10-2 Nm, N = 45, A = 1.8 x 10-2 m², B = 0.08 T. Rearranging the formula for current: I = τ / (N A B) = (2.5 x 10-2 Nm) / (45 * 1.8 x 10-2 m² * 0.08 T) = 2.5 / (45 * 1.8 * 0.08) A = 2.5 / 6.48 A ≈ 0.3858 A. This rounds to 0.39 A.
Hint
Recall the formula for torque on a current loop in a magnetic field: τ = NIABsinθ. For maximum torque, sinθ = 1.