A square loop of wire with 2.00 m sides is perpendicular to auniform magnetic fi

Question

A square loop of wire with 2.00 m sides is perpendicular to auniform magnetic field that points into the paper. Themagnitude of the field varies with time according to
B = 0.042 - 0.870 t with B in Teslas and t in seconds. a) What is the average EMFin the circuit in the interval of time between t = 0s and t = 2 s?b) What is the direction of the current through the resistor? A square loop of wire with 2.00 m sides is perpendicular to auniform magnetic field that points into the paper. Themagnitude of the field varies with time according to
B = 0.042 - 0.870 t with B in Teslas and t in seconds. a) What is the average EMFin the circuit in the interval of time between t = 0s and t = 2 s?b) What is the direction of the current through the resistor?

Explanation / Answer

a)the induced emf in the square loop is e = -N * (dB/dt) = -N * (d(B * A)/dt) = -N *A * (dB/dt) (dB/dt) = (d(0.042 - 0.870 t)/dt) = -0.870 or e = -N * A * (-0.870) = 0.87 * N * A N = 1 and A = a^2 where a = 2.00 m or A = (2.00)^2 = 4.00 m^2 or e = 0.87 * 1 * 4.00 = 3.48 V b)According to Lenz's law,the induced current in a loop is inthe direction that creates a magnetic field that opposes the changein magnetic flux through the area enclosed by the loop. That is,the induced current tends to keep the originalmagnetic flux trough the loop from changing.Therefore,the inducedcurrent through the resistor will be in the left direction.

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