A square conducting loop with side length a = 1.25 cm is placed at the center of

Question

A square conducting loop with side length a = 1.25 cm is placed at the center of a solenoid 40.0 cm long with a current of 3.90 A flowing through its 450 turns, and it is aligned so that the plane of the loop is perpendicular to the long axis of the solenoid. The radius of the solenoid is 5.00 cm.

(a) What is the magnetic flux through the loop?

_____Wb

(b) What is the magnitude of the average emf induced in the loop if the current in the solenoid is increased from 3.90 A to 14.0 A in 1.75 s?

______V

Explanation / Answer

Here,

side of square , a = 1.25 cm

a = 0.0125 m

distance ,d = 40 cm = 0.40 m

Current ,I = 3.90 A

N = 450

radius of solenoid, r = 5 cm

r = 0.05 m

a)

magnetic flux through the loop

magnetic flux through the loop = u0 * N * I/L * area

magnetic flux through the loop = 4pi *10^-7 * 450 * 3.90/0.40 * (0.0125)^2

magnetic flux through the loop = 8.615 *10^-7 Wb

the magnetic flux through the loop is 8.615 *10^-7 Wb

b)

for the induced average emf in the loop

I1 = 3.9 A

I2 = 14 A

t = 1.75 s

average emf = change in magnetic flux/time

average emf = u0 * N * (I1 - I2)/L * (time * area)

average emf = 4pi *10^-7 * 450 * (12 - 3.90)/(1.75 * 0.40) * (0.0125)^2

average emf = 1.022 *10^-6 V

the average emf is 1.022 *10^-6 V

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