A conducting bar of length l moves to the right on two frictionless rails as sho

Question

A conducting bar of length l moves to the right on two frictionless rails as shown in the figure below. A uniform magnetic field directed into the page has a magnitude of 0.320 T. Assume R = 8.80 Ohm and l = 0.340 m. (a) At what constant speed should the bar move to produce an 8.30-mA current in the resistor? m/s ________ m/s (b) What is the direction of the induced current? clockwise counterclockwise into the page out of the page (c) At what rate is energy delivered to the resistor? __________ mW (d) Explain the origin of the energy being delivered to the resistor. ______________

Explanation / Answer

a)
I=V/R where V=Blv
Therefore I=Blv/R

Then v=IR/Bl
I=8.3mA=0.0083A
R=8.8 ohms
B=0.320T
l=0.34m

so v=(0.0083*8.8)/(0.320*0.34) = 0.007304/0.1088 = 0.06713 m/s

b) clock wise

C)

rate at which energy delivered is
E=I^2R=(0.0083^2)*8.8 = 0.000606 MW

D) Origin of energy being delivered to resistor is from magnetic field.

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