Suppose you build a 1000-tum loop of wire, of diameter D = 105 cm, of negligible

Question

Suppose you build a 1000-tum loop of wire, of diameter D = 105 cm, of negligible resistance, attached to a resistor of resistance R = 14 ohm. In an attempt to generate electricity to heat the resistor, you spin the loop in the Earth's magnetic field. Assume that the Earth's magnetic field is horizontal and of strength B = 6.00 times 10^-5 Tesla. The loop stands up on its edge and spins about the vertical axis. If the loop revolves f = 60 times per second, what is the peak value of the emf felt by the resistor? What is the peak current through the resistor? What is the peak power that is dissipated by the resistor? What is the maximum speed at which any part of the loop is moving? 1.98times10^2 m/s

Explanation / Answer

here,

radius of coil, r = 105/2 = 52.5 cm = 0.525 m

Resistance, R = 14 Ohms

No of turns, n = 1000

Magnatic field, B = 6*10^-5 T

Time peroid of oscillation, t = 1/f = 1/60 = 0.017 s

Part A:
Peak Emf = n*B*A/t
Emf = 1000 * 6*10^-5 * pi*0.525^2 / 0.017
Emf = 3.056 V

Part B:
From Ohm's Law , Current = EMF/Resisatnce
I = 3.056/14
I = 0.218 A

Part C:
POwer, P = EMF * I
P = 3.056*0.218
P = 0.666 Watts

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