The figure P5.8 shows a conducting rod ab which makes contact with two metal rai

Question

The figure P5.8 shows a conducting rod ab which makes contact with two metal rails. The rails lie parallel to each other, separated by 75 cm, and are connected through a 18 resistor. The rod and rails can be assumed to have negligible resistance. The apparatus lies in a uniform magnetic field B = 1.2 T directed into the page. The rod is moved to the right at a constant speed v = 4 m/s.

a) Find the magnitude of the emf induced in the rod, and the magnitude and direction of the induced current.

b) Find the force required to keep the rod moving at this constant speed. (Assume friction is negligible.)

Explanation / Answer

Given that, Length of the rod l = 75 cm                               = 0.75 m Magnetic field B = 1.2 T Resistance R = 18 Speed of the rod v = 4 m/s a) We know that, The induced emf in the rod = B l v                                                             = ( 1.2 T )( 0.75 m )( 4 m/s )                                             = 3.6 V From Ohm's law V = IR Therefore       = B l v                         IR =  B l v The induced current in the rod is I =  ( B l v / R )                                                    I = ( 3.6 V /  18 )                                                     I = 0.2 amp Direction of the current is counter clock wise b to a. b) Force required to keep the rod moving at constant speed is                                                 F = B I l                                                 F = (1.2 T ) (0.2 amp)( 0.75 m )                                                 F = 0.18 N                                                                                                 F = (1.2 T ) (0.2 amp)( 0.75 m )                                                 F = 0.18 N                                                

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