A long, straight rail with a 5.5 cm spacing has no friction between the rail and

Question

A long, straight rail with a 5.5 cm spacing has no friction between the rail and a conducting rod that is pulled along the top of the rail. The rail is connected at the end the rod is being pulled away from by a 250 resistor. If the rod is being pulled at a constant velocity of 37 cm/s, and there is a uniform magnetic field coming up through the rails vertically of strength 1.5 T, what current is induced in the loop formed by the rod, the rails and the resistor? What direction is the current flowing in the system? Draw a careful diagram to indicate the direction of the field and indicate the direction of the current on this diagram.

Explanation / Answer

as per faraday's law, induced emf=-rate of change of total flux crossing the surface

=-rate of change of (B*A)

where B=1.5 T

A=0.055*x

where x is distance of the conducting rod from the 250 ohms resistor at any time t

hence emf induced=-d(1.5*0.055*x)/dt

=-1.5*0.055*dx/dt

but dx/dt=the speed of the rod being pulled=0.37 m/s

hence Vemf=-1.5*0.055*0.37==30.525 mV

part a:

magnitude of current induced=magnitude of voltage induced/resistance=30.525*10^(-3)/250=0.1221 mA

part b:

as per lenz'w law, the induced current should be such that it should oppose the source that induces it.

as area vector is perpendicular to the surface, flux linkage is increasing in the out of the page direction.

hence current should be in clockwise direction to satisfy the lenz's law.

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