A square wire loop with 3.00 m sides is perpendicular to a uniform magnetic fiel

Question

A square wire loop with 3.00 m sides is perpendicular to a uniform magnetic field, with half the area of the loop in the field, as shown below. The loop contains a 20.0 volt battery with a 225.0 ohm resistance in the circuit. If the magnitude of the field varies with time according to B(t) = (9.00 T/s)t - (5.60 T/s^2) * t^2 What is the induced emf in the circuit at 2.00 seconds? What is the total emf in the circuit at 2.00 seconds? What is the direction of the total current at that time (2 seconds)? What is the total current at that time (2 seconds)?

Explanation / Answer

Effective rea of the loop, A = 3^2/2

= 4.5 m^2

a) at t = 2 s

induced emf = -A*dB/dt

= -A*(9 - 5.6*2*t)

= -4*(9 - 5.6*2*2)

= 53.6 volts

b) Total emf = 20 + 53.6

= 73.6 volts

c) clockwise

d) I = total emf/R

= 73.6/225

= 0.327 A

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