A 21-cm -long, zero-resistance wire is pulled outward, on zero-resistance rails,

Question

A 21-cm -long, zero-resistance wire is pulled outward, on zero-resistance rails, at a steady speed of 1.0 m/s in a 0.10 T magnetic field (See the figure). On the opposite side, a 1.0 carbon resistor completes the circuit by connecting the two rails. The mass of the resistor is 52 mg .(Figure 1)

https://session.masteringphysics.com/problemAsset/1811760/4/jfk.Figure.25.P57.jpg

What is the induced current in the circuit?

What is the induced current in the circuit?

How much does the temperature of the carbon increase if the wire is pulled for 10 s? The specific heat of carbon is 710J/kgC.

Explanation / Answer

1. initially v = constant so

a = 0

i = V/R

V = B*v*L

i = B*v*L/R = 0.1*1*0.21/1

i = 0.021 Amp.

2.

F = i*L*B

F = 0.021*0.21*0.1

F = 4.41*10^-4 N

3.

P = V^2/R = i^2*R = 0.021^2*1.0 = 4.41*10^-4 W

Energy = power*time

in 10 s

E = 4.41*10^-4*10 = 4.41*10^-3 J

E = m*Cp*dT

dT = E/m*Cp = 4.41*10^-3/(52*10^-3*710)

dT = 1.19*10^-4 C

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