A circular loop of wire of radius 0.5 m and resistance 0.015 lies in the plane o

Question

A circular loop of wire of radius 0.5 m and resistance 0.015 lies in the plane of the page. A magnetic field directed out of the page increases in magnitude linearly with time from 0.0 T at t = 0 ms to 1.2 T at t = 6 ms.

What is the magnitude of the electromotive force that is induced in the loop?

What is the magnitude of the electric current that is induced in the loop?

What is the magnitude of the magnetic field that the current in the loop creates at the center of the loop?

At t = 3 ms, what is the magnitude of the total magnetic field at the center of the loop?

Explanation / Answer

a) Area = A = pi*r^2 = pi*0.5^2 = 0.785 m^2

E = A(dB/dt) = 0.785*(1.2/0.006) = 157 V

b) Current = I = E/R = 157/0.015 = 10466.67 A

c) B = uo*I/(2r) at the center of the loop

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