The conducting rod shown in the figure has length LL and is being pulled along h

Question

The conducting rod shown in the figure has length LL and is being pulled along horizontal, frictionless, conducting rails at a constant velocity. The rails are connected at one end with a metal strip. A uniform magnetic field B B, directed out of the page, fills the region in which the rod moves. Assume that L=4.32cmL=4.32cm, the speed of the rod is v=1.58msv=1.58ms, and the magnitude of the magnetic field is B=0.0307TB=0.0307T. The resistance of the rod is R=77.2R=77.2 and that the resistance of the rails and metal strip is negligibly small.

Calculate the current (in amperes) in the conducting loop.

NOTE: Careful of your units!

I=I=  A

Explanation / Answer

Here values given to us are;

Magnetic field strength, B = 0.0307 T

Breadth of loop, x = v*t

Velocity, v = 1.58 m/s

Length of loop, L = 0.0432 m

Area of loop, A = x*L = v*L*t

Angle between magnetic field and area vector, = 00

Resistance of loop, R = 77.2

So

Magnetic flux, B = A·B = AB cos = v*L*t*B*cos 0 = v*L*t*B

Induced e.m.f., e = -dB/dt = - v*L*B

Induced current, i = e/R = (B*L*v)/R = (0.0307*0.0432*1.58)/ 77.2 = 27.143*10-6 A = 27.143 A

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