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 = 2.37 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.
_____ Wb

(b) When the current is increased to 5.38 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?
__________ ms

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

counterclockwise

clockwise   

no current

Explanation / Answer

number of turns , n = 1200

diameter , d = 0.05 m

radius , r = 0.025 m

(a)

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

radius r = D/2 = 5/2 = 2.5 cm

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

flux = 4*3.14 * 10^-7 * 1200 * 2.37 * pi * 0.025^2 * 2

flux = 1.401 * 10^-5 T.m^2

----------------------------------------------------

(b) when I' = 5.38 A

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

flux' = 4pi * 10^-7 * 1200*2 * 5.38 * pi * 0.025^2

flux = 3.18* 10^-5 T.m^2

let the time be t

(flux' - flux) /t = voltage

t = (3.18 - 1.401 ) * 10^-5 /( 0.116)

t = 1.533 * 10^-4 s, the time taken 0.155 ms
--------------------------------------------

(c)

using Lenz's law, the direction of the induced current in the rectangular loop is clockwise

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