A pair of parallel wires of negligible resistance are 20 cm apart and located in

Question

A pair of parallel wires of negligible resistance are 20 cm apart and located in a uniform magnetic field of 1.0 T which is directed out of the plane of the paper. A resistance of 4.0 Ohm is connected between the left ends of the wire, and a conducting rod of negligible resistance is moved along the rails at a constant speed of 2.0 m/s to the right. Calculate: (a) the emf induced in the circuit; [0.4 volts] (b) the magnitude and direction of the induced current; [0.1 A, cw] (c) the force that has to be exerted on the conducting rod to keep it moving; [0.02 N, to right] (d) the rate at which work is being done by this force; [0.04 watt] (e) the power dissipated in the 4.0 Ohm resistor. [0.04 watt]

Explanation / Answer

step;1

Given that

speed of the rod v=2 m/s

length of the rod L=0.2 m

magnetic field B=1 T

resistance R=4 ohms

step;2

now we find the induced emf

the induced emf E=BLv=1*0.2*2=0.4 v

now we find the induced current

induced current i=E/r=0.4/4=0.1 A

now we find the force

force F=B^2L^2v/R=1^2*0.2^2*2/4=0.02 N

now we find the rate of work done

the work done W=B^2L^2v^2/R=1^2*0.2^2*2^2=0.04 Wait

now we find the power dissipated by resistor

the power dissipated =v^2/R=0.4^2/4=0.04 W

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