A flat circular wire loop of area 0.25 m² carries a current of 5.0 A.This coil lies on a horizontal table with the current flowing in the counterclockwise direction when viewed from above.At this point,the earth's magnetic field is 1.2 × 10^-5 T directed 60° below the horizontal.What is the magnitude of the torque that the earth's magnetic field exerts on this loop? A)2.5 × 10^-6 N ∙ m B)5.0 × 10^-6 N ∙ m C)7.5 × 10^-6 N ∙ m D)1.0 × 10^-5 N ∙ m

Question

Quizplus · Accepted Answer

The torque on a wire loop in a magnetic field is given by:
τ = NABsinθ, 
where N is the number of turns, A is the area, B is the magnetic field, and θ is the angle between the magnetic field and the normal to the plane of the loop. Here, N = 1, A = 0.25 m^2, B = 1.2 × 10^-5 T, sinθ = sin(60°) = √3 / 2. Therefore, 
τ = (1)(0.25)(1.2 × 10^-5)(√3 / 2) = 7.5 × 10^-6 N∙m. 
So, the correct option is C.

A Flat Circular Wire Loop of Area 0