A rolling axle is being pushed so that it rolls along a set of parallel rails at

Question

A rolling axle is being pushed so that it rolls along a set of parallel rails at a constant speed of v = 2.50 m/s. The distance between the rails is 0.75 m (this is the same length as the axle), and as shown in the diagram, there is a magnetic field acting straight downward with a strength of B = 0.42 T. A resistor, R = 0.600 Ohm is attached between the rails at points a and b. Assume the wheels make good electrical contact with the rails, and both wheels, axle and rails have negligible resistance. What is the induced current in the resistor? How much force is required to push the axle along at constant speed? Which end of the resistor a or b is at the higher electrical potential? After the axle rolls past the resistor, does the current through the resistor switch directions?

Explanation / Answer

a) induce emf = BvL = 0.42 x 2.5 x 0.75

emf = 0.7875 volts

as resistance R =0.6 ohm

i = emf /R = 0.7875/0.6 = 1.31 A

b) due to this current i

foce F = B i L

F = 0.42 x 1.31 x 0.75

F = 0.413 N

c) b will be higher

right hand thumb rule

( as the flux in increasing so the induce current direction willl be in such way it will oppose of this change s0 current will flow CW

d) yes it wil change

now

right hand thumb rule

( as the flux in decreasing so the induce current direction willl be in such way it will oppose of this change s0 current will flow ACW

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