A solenoid with 1200 turns per meter has a diameter of 5.00 cm. A current I = 2.

Question

A solenoid with 1200 turns per meter has a diameter of 5.00 cm. A current I = 2.46 A flows in the counterclockwise direction 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 the loop.

(b) When the current is increased to 5.37 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?

(c) What is the direction of the induced current in the rectangular loop as viewed from the location P?

Explanation / Answer

here,

number of turns , n = 1200

diameter , d = 0.05 m

radius , r = 0.025 m

I = 2.46 A

(a)

the magnitude of the magnetic flux , flux = B * area* N

flux = u0 * n* I * pi * r^2 * N

flux = 1.26 * 10^-6 * 1200 * 2.46 * pi * 0.025^2 * 2

flux = 1.46 * 10^-5 T.m^2

(b)

when I' = 5.37 A

flux' = u0 * n* I' * pi*N * r^2

flux' = 1.26 * 10^-6 * 1200*2 * 5.37 * pi * 0.025^2

flux = 3.186 * 10^-5 T.m^2

let the time be t

(flux' - flux) /t = voltage

(3.186 - 1.46 ) * 10^-5 /( 0.116) = t

t = 1.49 * 10^-4 s

the time taken is 1.49 * 10^-4 s

(c)

using Lenz's law

the direction of the induced current in the rectangular loop is clockwise

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