A 20-cm. long, zero resistance wire is pulled outward on zero resistance rails a

Question

A 20-cm. long, zero resistance wire is pulled outward on zero resistance rails at a steady speed of 1.0 m/s in a 0.1 T magnetic field, as in the figure. On the opposite side, a 1.0 ohm carbon resister completes the circuit by connecting the two rails. The mass of the resistor is 50 mg. (a) What is the induced current in the circuit? (b) How much force is required to pull the wire at this speed? (c) How much does the temperature of the carbon increase if the wire is pulled for 10s? The specific heat of carbon is 710 J/kg K.

Explanation / Answer

Given:

L = 20-cm, v = 1 m/s, B = 0.1 T, R = 1 , m = 50 mg, c= 710 J/kg · C°, t = 10 s

(a) Using
I = BLv/R = 0.02 A

(b) Using
F = IBL = 0.0004 N

(c) Using
Power = I2R = mc*T
Hence T = 0.01127 C°

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