Two coils have the same number of circular turns and carry the same current. Eac

Question

Two coils have the same number of circular turns and carry the same current. Each rotates in a magnetic field as in the figure below. Coil 1 has a radius of 4.3 cm and rotates in a 0.22-T field. Coil 2 rotates in a 0.42-T field. Each coil experiences the same maximum torque. What is the radius (in cm) of coil 2? The 1600-turn coil in a dc motor has an area per turn of 1.1 times 10^-2 m^2. The design for the motor specifies that the magnitude of the maximum torque is 5.8 N middot m when the coil is placed in a 0.19 T magnetic field. What is the current in the coil?

Explanation / Answer

T = mu * B , Tmax = mu B = N I A B

N I A1 B1 = N I A2 B2

A1 B1 = N I A2 B2

pi * r12 * B1 = pi * r22 * B2

r12 * B1 = r22 * B2

(4.3 cm)2 * (0.22 T) = r22 * (0.42 T)

r2 = 3.11 cm

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