a single loop of wire is located at the center of a long solenoid of radius R wh

Question

a single loop of wire is located at the center of a long solenoid of radius R which has n turns per unit length and carries a current I. The loop is coaxial with the solenoid and has a radius a. n = 3000/m a = 3cm I = 5A

A. the magnetic flux passing through the loop is? (the answer is 53 u*Wb i just need to see the work to get the answer)

B. if the current in the solenoid is not constant but varies as I = I,m cos wt, where I,m = 5A and w = 101 rad/s, the amplitude of the emf induced in the loop will be? ( the answer is 5.4mV i need to see the work on how to get the answer)

Explanation / Answer

here,

radius , a = 3 cm

a = 0.03 m

current , I = 5 A

number of turns , n = 3000 / m

(a)

the magnetic flux passing through the loop is , flux = u0 * n * I * A

flux = u0 * 3000 * 5 * pi * 0.03^2

flux = 5.33 * 10^-5 Wb

the magnetic flux passing through the loop is 53 u Wb

(b)

I = Im * cos(w*t)

w = 101 rad/s

Vpeak = n * B * A * w

Vpeak = n * u0 * Im * A * w

Vpeak = 3000 * u0 * 5 * pi * 0.03^2 * 101

Vpeak = 5.38 * 10^-3 V

the amplitude of the induced emf in the loop is 5.3 mV

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