A 2-meter long solenoid, which may be considered to be infinitely long, is unifo

Question

A 2-meter long solenoid, which may be considered to be infinitely long, is uniformly winded 6000 turns by a wire carrying a current i1. The diameter of the solenoid in 20 cm.

(a) Inside the solenoid, another circular wire loop of diameter 15 cm and resistance 600 omega is oriented with its normal parallel to the solenoid axis. The cross-section view is given in the figure. At the moment when the solenoid current i1 is 4A and increases at a rate of +10 A/s, what is the magnitude of the induced current i2 in the circular wire loop? Show the direction of the induced current i2 if the solenoid current i1 runs clockwise.

A 2-meter long solenoid, which may be considered to be infinitely long, is uniformly winded 6000 turns by a wire carrying a current i1. The diameter of the solenoid in 20 cm. Inside the solenoid, another circular wire loop of diameter 15 cm and resistance 600 omega is oriented with its normal parallel to the solenoid axis. The cross-section view is given in the figure. At the moment when the solenoid current i1 is 4A and increases at a rate of +10 A/s, what is the magnitude of the induced current i2 in the circular wire loop? Show the direction of the induced current i2 if the solenoid current i1 runs clockwise.

Explanation / Answer

a)

emf = d(phi)/dt

==> emf = A dB/dt

==> emf = (pi r^2) d(u N/L i)/dt

==> emf = pi r^2 u N/L di/dt

==> emf = 3.1416*0.15*0.15*4*3.1416e-7*6000/2*10

==> emf = 0.0026648 V

i2 = emf/R = 0.0026648/600 = 4.44 x 10^-6 A

Direction: counterclockwise

According to the Lenz's law, induced current is in a direction to reduce the magnetic field.

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