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

Question

A square wire loop with 3.00 m in 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 25.0 ohm resistance in the circuit. If the magnitude of the Held varies with time according to B(t) = (9.00 T/s)t - (2.60 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

9.

a) Induced emf =rate of change of flux

        = d (N B A)/dt

      = N A dB/dt

     = 1 * (L^2 /2 ) (9 - 5.2t)

e = 40.5 - 23.4t

at t = 2 sec

e = 40.5 - 2(23.4) =- 6.3 Volt

so induced emef is 6.3 Volt.

b) total emf = 20 + 6.3 = 26.3 volt

c) induced curent = e / R = 6.3 / 25 = 0.252 A

d) total current = 26.3 / 25 = 1.052 A

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