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The resistance of a metal wire 1m long is measured and is found to be 0.1Ω....

The resistance of a metal wire 1m long is measured and is found to be 0.1Ω. The wire is then formed into a circular ring, with the two ends of the wire welded together so that the joint has negligible resistance. A uniform magnetic field perpendicular to the plane of the ring increases at a constant rate from 0 Tesla to 2 Tesla. How much charge moves through the joint in the metal ring during this process?

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Answer #1

Let time taken be t,

induced voltage = Area*dB/dt

V = pi*r^2*B/t

= pi*(1/(2pi))^2*2/t

current i = V/R

charge q = i*t = pi*(1/(2pi))^2*2/t*t/R

= pi*(1/(2pi))^2*2/0.1

= 1.59 C answer

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