The drawing shows a copper wire (negligible resistance) bent into a circular sha

Question

The drawing shows a copper wire (negligible resistance) bent into a circular shape with a radius of 0.59 m. The radial section BC is fixed in place, while the copper bar AC sweeps around at an angular speed of 13 rad/s. The bar makes electrical contact with the wire at all times. The wire and the bar have negligible resistance. A uniform magnetic field exists everywhere, is perpendicular to the plane of the circle, and has a magnitude of 4.5 x 10-3 T. Find the magnitude of the current induced in the loop ABC.

The drawing shows a copper wire (negligible resistance) bent into a circular shape with a radius of 0.59 m. The radial section BC is fixed in place, while the copper bar AC sweeps around at an angular speed of 13 rad/s. The bar makes electrical contact with the wire at all times. The wire and the bar have negligible resistance. A uniform magnetic field exists everywhere, is perpendicular to the plane of the circle, and has a magnitude of 4.5 x 10-3 T. Find the magnitude of the current induced in the loop ABC.

Explanation / Answer

The formula for the induced EMF is

= BA/t = IR

The area is changing from basically zero to a full circle. Since the angula speed f the sweep is 13 rad/s, and we know one full circle is 2 rad. The time required to make one full circle is found by

= t

t = 2/13 = .4833 sec

So

(4.5 X 10-3)()(.59)2/(.4833) = (I)(3)

I = 3.39 X 10-3 A which is 3.39 mA

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