What current must be maintained in a square loop (50 cm on a side) to create a torque of 1.0 N ⋅ m about an axis through its center and parallel to one of its sides when a magnetic field of magnitude 70 mT is directed at 40° to the plane of the loop?
A) 66 A
B) 89 A
C) 61 A
D) 75 A
E) 37 A

Question

Quizplus · Accepted Answer

The torque on a square loop in a magnetic field is given by:

τ = NABsinθ

where N is the number of turns in the loop, A is the area of the loop, B is the magnitude of the magnetic field, and θ is the angle between the magnetic field and the normal to the plane of the loop.

For a square loop, A = (50 cm)² = 2500 cm² = 0.25 m².

The torque is given as 1.0 N⋅m.

The magnetic field is given as 70 mT = 0.07 T.

The angle between the magnetic field and the normal to the loop is 40°.

We can rearrange the formula to solve for the current:

I = τ/(NABsinθ)

Plugging in the given values, we get:

I = (1.0 N⋅m)/[(1)(0.25 m²)(0.07 T)sin(40°)]

I ≈ 75 A

So the answer is D) 75 A.

What Current Must Be Maintained in a Square Loop (50