A square wire with 2 m sides is perpendicular to a uniform magnetic field, with

Question

A square wire with 2 m sides is perpendicular to a uniform magnetic field, with half the area of the loop in the field as shown in the figure. The loop contains a 20 V battery with negligible resistance. If the magnitude of the field varies with time according to

B = 1.0410 - 0.8600 t

with B in teslas and t in seconds, what is the total emf in the circuit?

***** I got 1.72 V but that is not correct. A clear solution would be very helpful.

A square wire with 2 m sides is perpendicular to a uniform magnetic field, with half the area of the loop in the field as shown in the figure. The loop contains a 20 V battery with negligible resistance. If the magnitude of the field varies with time according to B = 1.0410 - 0.8600 t with B in teslas and t in seconds, what is the total emf in the circuit?

Explanation / Answer

flux through the circuit = L^2B /2

emf = -L^2/2 dB/dt

dB/dt = -0.86

emf = -2^2/2 * -0.86 = 1.72 V

total emf = 20 + 1.72 = 21.72 V

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