A circular wire loop of radius 1.4 cm is placed in a magnetic field of magnitude...

A circular wire loop of radius 1.4 cm is placed in a magnetic field of magnitude 2.3 T. If the magnetic field goes to zero in a time of 5 s, what is the magnitude of the current induced in the loop? The wire has a diameter of 2 mm, and the resistivity of copper is 1.7 x 10-8 Ohm-m.

Solutions

Expert Solution

According to Lenz's law, the voltage induced in the loop, V = d/dt
is the flux passing through the coil, = B x Area of the loop
B = 2.3 T
A1 = R² = x (0.014)² = 6.157 x 10^-4 m².
= BA1 = 1.416 x 10^-3.
B becomes zero in 5 seconds, dt = 5 s
V = d/dt = 2.832 x 10^-4 V

According to Ohm's law, V = IR
R = L/A
= 1.7 x 10^-8 Ohm-m.
L = 2R = 0.028 m.
A2 = r² = x (1 x 10^-3)² = x 10^-6 m².
R = 4.76 x 10^-4 Ohm

I = V/R = 2.832 x 10^-4 V / 4.76 x 10^-4 Ohm = 0.595 A

genius_generous answered 1 year ago

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