A 99-turn square coil of side 20.0 cm rotates about a vertical axis at omega = 1

Question

A 99-turn square coil of side 20.0 cm rotates about a vertical axis at omega = 1.67 times 10^3 rev/min as indicated in the figure below. The horizontal component of Earth's magnetic field at the coil's location is equal to 2.00 times 10^5 T. (a) Calculate the maximum emf induced in the coil by this field. mV (b) What is the orientation of the coil with respect to the magnetic field when the maximum emf occurs? The plane of the coil is perpendicular to the magnetic field. The plane of the coil is oriented 45 degree with respect to the magnetic field. The plane of the coil is parallel to the magnetic field.

Explanation / Answer

(A) emf induced = rate of change of magentic flux

= N B A w sin(wt)

w = 1.67 x 10^3 x 2pi rad / 60 s = 174.88 rad/s

emf_max = N B A w = 99 x 0.20^2 x 2 x 10^-5 x 174.88

= 0.01385 Volt OR 13.85 mV

(B) plane of coil is perpendicular to the magnetic field

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