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 0.43 m. The radial section BC is fixed in place, while the copper bar AC sweeps around at an angular speed of 20 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 3.3 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 0.43 m. The radial section BC is fixed in place, while the copper bar AC sweeps around at an angular speed of 20 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 3.3 x 10-3 T. Find the magnitude of the current induced in the loop ABC. (into paper ire 3.02 NumberT-.0020339 Units A

Explanation / Answer

Given data : r = 0.43 m

                   = 20 rad/s

                   R = 3.00

                   B = 3.3 x10-3 T

= -N.(B.A)/t = -NB.A/t = -N.B.(r2)/T with = 2/T

= - N.B..r2/2

I.R = -N.B..r2/2

I = NBr2/(2R) = 1*(3.3 x10-3*20*0.432)/(2*3.0)

I = 2.03x10-3 A = 2.03 mA

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