Question

A square, single-turn wire loop ℓ = 1.00 cm on a side is placed inside a solenoid that has a circular cross section of radius r = 3.00 cm, as shown in the end view of the figure below. The solenoid is 24.0 cm long and wound with 122 turns of wire. (a) If the current in the solenoid is 2.35 A, what is the magnetic flux through the square loop? T · m2 (b) If the current in the solenoid is reduced to zero in 3.45 s, what is the magnitude of the average induced emf in the square loop? V

Answer 1

(a)

l = length of the side of the square = 1 cm = 0.01 m

A = area of the square loop = l² = 0.01 x 0.01 = 10^-4 m²

L = length of the solenoid = 24 cm = 0.24 m

N = number of turns = 122

n = number of turns per unit length = N/L = 122/0.24 = 508.33

i = current in the solenoid = 2.35 A

magnetic field through the solenoid is given as

B = $\mu _{o}$ ni

magnetic flux though the square loop is given as

$\phi$ = B A

$\phi$ = $\mu _{o}$ niA

inserting the values

$\phi$ = (12.56 x 10^-7) (508.33) (2.35) (10^-4)

$\phi$ = 1.5 x 10^-7 Wb

b)

$\Delta$i = change in current = 0 - 2.35 = - 2.35 A

$\Delta$t = time interval = 3.45 sec

Induced emf is given as

E = - $\mu _{o}$ nA($\Delta$i/$\Delta$t )

E = - (12.56 x 10^-7) (508.33) (10^-4) (- 2.35/3.45 )

E = 4.35 x 10^-8 Volts