A conducting rod whose length is 25.0 cm is placed on a U-shaped metal wire that

Question

A conducting rod whose length is 25.0 cm is placed on a U-shaped metal wire that has a resistance R of 8.00 ohms. The wire and the rod are in the plane of the paper. A constant magnetic field of strength  0.4 T is applied perpendicular and into the paper. An applied force moves the rod to the right with a constant speed of 6.00 m/s.

a) Find the magnitude of the induced emf in the wire.

b) Find the magnitude and direction of the induced current in the wire.

c) Find the magnitude of the force required to keep the rod moving with constant speed.

Explanation / Answer

The induced EMF = change in flux linked with the circuit.

Since Flux phi = N x A X B where N = # of turns, A = area and B = magnetic field intensity,

The rate of change of this is the rate of change of area swept by the rod which is equal to length of rod X velocity

The change in magnetic flux linked to the circuit in 1 s = 0.25 m X 6 m/s X 0.4 T = 0.60 V

The current = 0.60 V / 8 = 0.075 A or 75 mA

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