A circular conducting ring with radius r0 = 0.0420 m lies in the xy-plane in a r

Question

A circular conducting ring with radius r0 = 0.0420 m lies in the xy-plane in a region of uniform magnetic field = B[1 - 3(t/t0)2 + 2(t/t0)3] . In this expression, t0 = 0.0100 s and is constant, t is time, is the unit vector in the +z-direction, and B = 0.0840 T and is constant. At points a and b there is a small gap in the ring with wires leading to an external circuit of resistance R = 12.0 f1. There is no magnetic field at the location of the external circuit. (a) Derive an expression, as a function of time, for the total magnetic flux 0B through the ring. (Use any variable or symbol stated above as necessary. Do not substitute numerical values; use variables only.) (b) Determine the emf induced in the ring at time t = 5.00 X 10^-3 s. Epsilon = .066 X V What is the polarity of the emf? clockwise counterclockwise (c) Because of the internal resistance of the ring, the current through R at the time given in part (b) is only 3.00 mA. Determine the internal resistance of the R = [ ] omega (d) Determine the emf in the ring at a time t = 1.21 X 102 s.

Explanation / Answer

a)

FLUX=B.A

=B0(1-3(t/t0)2+2(t/t0)3)*3.14*0.0422

=0.0055B0(1-3(t/t0)2+2(t/t0)3)k

E=-d(pi)/dt

first we need to find out flux at 0.01seconds

=0.0055*0.084*(1-4.392+3.543)

=6.97*10-5wb

E=6.97*10-5/1.21*10-2

=5.76mV

I=V/R+R1

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