5. OSColPhys2016 232.WA.014. Notes O Ask k Your Teacher turns per meter has a di

Question

5. OSColPhys2016 232.WA.014. Notes O Ask k Your Teacher turns per meter has a diameter of 8.00 cm. A current 1-2.48 A flows in the counterclockwise direction in the 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. What is the area over which the flux has a non-zero value? wb (b) When the current is increased to S.sS A, the magnitude of the induced emf in the rectangula take for the current to get to this value? of the induced emf in the rectangular loop is 116 mV. How long did it

Explanation / Answer

Given,

n = 1200 tuns/m ; d = 8 cm => r = 4 cm = 0.04 m

I = 2.48 A ; CCw ; L = 16 cm = 0.16 m ; w = 12.5 cm = 0.125 m ; N = 2

a)We know that the magnetic flux through a surface is given by:

phi = B A

B field of a solenoid is:

B = u0 n I

B = 4 x 3.14 x 10^-7 x 1200 x 2.48 = 3.74 x 10^-3 T

A = Area of rectangular loop

A = L W = 0.16 x 0.125 = 0.02 m^2

Area of Solenoid is

As = pi r^2 = 3.14 x 0.04^2 = 0.00502 m^2

phi = B A = 3.74 x 10^-3 x 0.005 = 1.88 x 10^-5

phi = 1.88 x 10^-5 Wb

b)I = 5.5 A ; emf = 116 mV

Let t be the time taken

we know that the induced emf is given by:

emf = d(phi)/dt => (phi2 - phi1)/t

t = (phi2 - phi1)/emf

phi2 = B2 A

phi = 2 x 4 x 3.14 x 10^-7 x 1200 x 5.5 x 0.00502 = 8.32 x 10^-5 Wb

(2 times, because there are N = 2 loops)

t = (8.32 - 1.88) x 10^-5/116 x 10^-3 = 0.555 ms

Hence, t = 0.555 ms

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