A 17-cm-long, zero-resistance slide wire moves outward, on zero-resistance rails

Question

A 17-cm-long, zero-resistance slide wire moves outward, on zero-resistance rails, at a steady speed of 10 m/s in a 0.14 T magnetic field. (See Figure 33.26 in the textbook). On the opposite side, a 1.5 carbon resistor completes the circuit by connecting the two rails. The mass of the resistor is 58 mg .

Part A

What is the induced current in the circuit?

Part B

How much force is needed to pull the wire at this speed?

Part C

If the wire is pulled for 10 s, what is the temperature increase of the carbon? The specific heat of carbon is 710 J/(kgK).

Explanation / Answer

Part A

The induced emf is e= Blv = 0.14 x 0.17x10 =0.238V

The induced current is, i = e/R = 0.238V/ 1.5? = 0.159A

Part B

F= Bil = 0.14 x 0.159x 0.17 = 3.78x10-3 N

Part C

Power, P = I2R = 0.1592 x 1.5 = 0.0379J

E= P/t = 0.0379J/ 10s = 3.79x10-3 J/s

Energy stored, E = mc?T

?T = E/mc = 3.79x10-3/ (5.8x10-5 x710) = 0.0919OC

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