A solenoid with 1200 turns per meter has a diameter of 4.00 cm. A current I = 2.

Question

A solenoid with 1200 turns per meter has a diameter of 4.00 cm. A current I = 2.58 A flows in the counterclockwise direction (when viewed from location P) in the solenoid. A rectangular loop of length L = 16.0 cm, width w = 12.5 cm, and 2 turns is centered on the axis of the solenoid.

(a) Find the magnitude of the magnetic flux through one turn of the rectangular loop.

(b) When the current is increased to 5.40 A, the magnitude of the induced emf in the rectangular loop is 116 mV. How long did it take for the current to get to this value? (Answer in miliseconds)

Explanation / Answer

Here,

N = 1200

I = 2.58 A

a)

magnitude of magnetic flux through one turn = pi * (0.04/2)^2 * magnetic field

magnitude of magnetic flux through one turn = pi * (0.04/2)^2 * 4pi *10^-7 * 1200 * 2.58

magnitude of magnetic flux through one turn = 4.89 *10^-6 T.m^2

b)

let the time taken is t

induced emf = change in flux/time

116 *10^-3 = 2 * pi * (0.04/2)^2 * 4pi *10^-7 * 1200 * (5.40 -2.58)/t

solving for t

t = 9.21 *10^-5 s

the time taken to change the flux is 9.21 *10^-5 s

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