A circular loop of wire with radius 0.0230m and resistance 0.400 A circular loop

Question

A circular loop of wire with radius 0.0230m and resistance 0.400

A circular loop of wire with radius 0.0230 m and resistance 0.400 ohm is in a region of spatially uniform magnetic field, as shown in the following figure(Figure 1). The magnetic field is directed into the plane of the figure. At t = 0, B = 0. The magnetic field then begins increasing, with B(t) = (0.320 T/s^3) t^3 What is the current in the loop (magnitude) at the instant when 1.28 T ? Express your answer with the appropriate units. What is the direction of the current in the loop? clockwise counterclockwise

Explanation / Answer

Emf = d(phi)/dt

i = Emf/R

phi = B*A

i = pi*r^2*dB/(dt*R)

dB/dt = 3*0.32*t^2

time when B = 1.28 T will be

1.28 = 0.32*t^3

t = (1.28/0.32)^(1/3) = 1.587 sec

at this time

dB/dt = 3*0.32*1.587^2 = 2.417 T/sec

i = pi*0.0230^2*2.417/0.4 = 0.01 Amp.

B.

since the magnetic field is into the plane, so direction of current will be clockwise from len'z law.

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