In the figure below, the rolling axle, 1.43 m long, is pushed along horizontal rails at a constant speed&nbsp;v=3.36m/s.A resistor&nbsp;R=0.325&nbsp;ohm is connected to the rails at points a and b, directly opposite each other. (The wheels make good electrical contact with the rails, and so the axle, rails, and R form a closed-loop circuit. The only significant resistance in the circuit is R.) There is a uniform magnetic field&nbsp;B=0.0850Tvertically downward. Calculate the induced current I in the resistor and what horizontal force F is required to keep the axle rolling at constant speed?

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In the figure below, the rolling axle, 1.43 m long, is pushed along horizontal rails at a constant speed&amp;nbsp;v=3.36m/s.A resistor&amp;nbsp;R=0.325&amp;nbsp;ohm is connected to the rails at points a and b, directly opposite each other. (The wheels make good electrical contact with the rails, and so the axle, rails, and R form a closed-loop circuit. The only significant resistance in the circuit is R.) There is a uniform magnetic field&amp;nbsp;B=0.0850Tvertically downward. Calculate the induced current I in the resistor and what horizontal force F is required to keep the axle rolling at constant speed?

2k1enyvp · Accepted Answer

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Jeffrey Jordon · Accepted Answer

Given that  Length of the rolling axle, l=1.43 m  Speed of the axle, v=3.36 m/s  Resistance of the resistor R=0.325  Magnitude of the uniform magnetic field, B=0.0850 T  When a rod of length l moving with velocity v in the uniform magnetic field B, then the induced emf produced in the rod is given by  ϵ=Blv  From the ohm&#039;s law, ϵ=iR  here, the current induced in the resistor =i  Then, iR=Blv  Threfore, the induced current produced in the resistor is  i=BlvR  =(0.0850T)(1.43 m)(3.36 m/s)(0.325)  =1.256 A  The horizontal force F required to keep the axle rolling at constant speed is given by  F=Bil  =(0.0850 T)(1.256 A)(1.43 m)  =0.152 N

In the figure below, the rolling axle, 1.43 m long, is pushed along horizontal rails at a constant speed v = 3.36 m/s.

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