A circular coil of wire has a radius of 0.550m , 19 turns, and a total resistanc

Question

A circular coil of wire has a radius of 0.550m , 19 turns, and a total resistance of 1.57ohms . The coil lies in the xy-plane. The coil is in a uniform magnetic field B that is in the -z direction, which is directed away from you as you view the coil. The magnitude B of the field depends on time as follows: increases at a constant rate from 0 at t=0 to 0.850T at t1 = 0.530s ; is constant at 0.850T from t1= 0.530s to t2 = 0.95s ; decreases at a constant rate from 0.850T at t2 = 0.95s to 0 at t3 = 2.11s .

A) What is the maximum induced electric field magnitude in the coil during the t=0 to 2.11s time interval? Assume that the uniform magnetic field does have a circular symmetry about the axis of the coil.

B) What is the maximum induced EMF in the coil during the t=0 to 2.11s time interval?

Please include the process you used and numerical answers if possible.

Explanation / Answer

Total magnetic flux. B*pi*r^2*N=B*18.1 U=-(B*18.1)'=-B'*18.1=E*2piR. so E=-B'*18.1/2piR=-5.2*B' --------- B' from t0 to t1 0.85/0.53=1.6(T/s) B' from t1 to t2. 0 B' from t2 to t3 0.85/(2.11-0.95)=0.73(T/s). ---------- so Emax=5.2*1.6=8.3(N/C) so Umax=8.3*2pi*R=28.8(V)

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