A rectangular loop rotates with a constant angular velocity about an axis as sho

Question

A rectangular loop rotates with a constant angular velocity about an axis as shown. It makes one complete rotation in 0.02 s. The magnetic field lines are straight and parallel as shown. They are perpendicular to the axis of rotation. The lengths are c= 0.8 m and d= 4.1 m, the strength of the magnetic field is 0.05 T. The total resistance of the loop is 122 .

1.) What is the maximum current I through the loop?

2.) At the instant when the current is a maximum, what torque (magnitude) must be applied by outside forces to keep the loop rotating at a constant angular velocity?

Explanation / Answer

w = 2pi / 0.02 rad/s =314.16 rad/s

1) Induced EMF E = 2Bdcw

= 2 x 0.05 x 4.1 x 0.8 x 314.16 = 103.04 V

I = e /R = 103.04 / 122 = 0.845 A

2) torque = 2BIcd

= 2 x 0.05 x 0.845 x 0.8 x 4.1 = 0.278 Nm

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