In the figure, the rolling axle, 1.49 m long, is pushed along horizontal rails a

Question

In the figure, the rolling axle, 1.49 m long, is pushed along horizontal rails at a constant speed v = 3.04 m/s. A resistor R = 0.395 omega 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 B = 8.90x10^-2 T vertically downward. Calculate the induced current I in the resistor. What horizontal force Fb is required to keep the axle rolling at constant speed? Calculate the size of the potential difference between point a and point b.

Explanation / Answer

given,

length of axle = 1.49 m

speed = 3.04 m/s

resistance = 0.395 ohm

magnetic field = 8.9 * 10^-2 T

change in area = length * speed

change in area = 1.49 * 3.04

change in area = 4.5296 m^2/s

induced emf = magnetic field * change in area

induced emf = 8.9 * 10^-2 * 4.5296

induced emf = 0.403 V

by ohm's law

v = I * R

0.403 = I * 0.395

induced current in the resistor = 1.02 A

force on the axle due to magnetic field = magnetic field * current * length

force on the axle due to magnetic field = 8.9 * 10^-2 * 1.02 * 1.49

force on the axle due to magnetic field = 0.1352 N

since the velocity is constant so net force will be 0

so force required to keep the axle rolling at constant speed = 0.1352 N

potential difference between point a and b = 0.403 V

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