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In Figure $\mathrm{P} 20.65$ the rolling axle of length 1.50 $\mathrm{m}$ is pushed along horizontal rails at a constant speed $v=3.00 \mathrm{m} / \mathrm{s}$ . A resistor $R=0.400 \Omega$ is connected to the rails at points $a$ and $b,$ directly opposite each other. (The wheels make good electrical contact with the rails, so the axle, rails, and $R$ form a closed-loop circuit. The only significant resistance in the circuit is $R$ ) A uniform magnetic field $B=0.800 \mathrm{T}$ is directed vertically downward. (a) Find the induced current I in the resistor. (b) What horizontal force $\overrightarrow{\mathbf{F}}$ is required to keep the axle rolling at constant speed? (c) Which end of the resistor, $a$ or $b,$ is at the higher electric potential? (d) After the axle rolls past the resistor, does the current in $R$ reverse direction? Explain your answer.

a. 9.00 \mathrm{A}

b. 10.8 \mathrm{N}

c. b

d. \text { See explanation for result. }

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Rutgers, The State University of New Jersey

Numerade Educator

University of Washington

McMaster University

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