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 0.536 m.The radial sectionBCis fixed in place, while the copper barACsweeps around at an angular speed of 15.9 rad/s. The bar makes electrical contact with the wire at all times. The wire and the bar have negligible resistance. AssumeR= 3.02 ?. A uniform magnetic field exists everywhere, is perpendicular to the plane of the circle, and has a magnitude of 3.63E-3 T. Calculate the magnitude of the current induced in the loopABC.

The drawing shows a copper wire (negligible resistance) bent into a circular shape with a radius of 0.536 m.The radial sectionBCis fixed in place, while the copper barACsweeps around at an angular speed of 15.9 rad/s. The bar makes electrical contact with the wire at all times. The wire and the bar have negligible resistance. AssumeR= 3.02 ?. A uniform magnetic field exists everywhere, is perpendicular to the plane of the circle, and has a magnitude of 3.63E-3 T. Calculate the magnitude of the current induced in the loopABC.

Explanation / Answer

Given data : r = 0.536 m

                   = 15.9 rad/s

                   R = 3.02

                   B = 3.6x10-3 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.(3.6x10-3.15.9.0.5362)/(2.3.02)

I = 2.72x10-3 A = 2.72 mA

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