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Question

A circular copper disc, of radius 5 cm, rotates with 10 rad/s about an axis through its center and perpendicular to the disc. A uniform magnetic field of 2 T acts perpendicular to the plane of the disc. What is the induced current in the disc if a resistor of resistance 1 Ω is connected between the midpoint of a radius and the center of the disc?

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Solution

Given:
Radius of disc, r=0.05 m
Angular speed, ω=10 rad/s
Magnetic field, B=2 T
Resistance, R=1 Ω

Emf induced between the midpoint of a radius and the center of the disc is,

E=Bωl22=Bωr28 (l=r/2)

=2×10×0.0528=6.25×103 V

Now, the current flowing through the resistor is,

i=ER=6.25×1031=6.25×103 A

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