Question

Find the maximum torque on a 100-turn square loop of a wire of 10.0 cm on a side that carries 15.0 A of current in a 2.00-T field.​

Answer 1

The maximum torque is 30 Nm.

Given:

Number of turns, N = 100

Length of wire = 10 cm = 0.1 m

Current, I = 15 A

Magnetic field, B = 2 T

To Find:

The maximum torque =?

Solution:

The torque τ on the loop can be found by using the formula

τ = NIABsinθ

where N = the number of turns,  

I = current,  

A = the area of the loop,  

B = magnetic field strength, and  

θ = angle between the perpendicular to the loop and the magnetic field.

Area of loop = 0.1 × 0.1 = 0.01 m².

Maximum torque occurs when θ is 90°.

Putting the given values in the question, we get

τ = 100 × 15 × 0.01 × 2 × sin90

τ = 30 × sin90

τ = 30 (sin90 =1)

Hence, the maximum torque is equal to 30 Nm.

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