1) A conducting loop of area 220 cm2 and resistance 13 ? lies at right angles to

Question

1) A conducting loop of area 220 cm2 and resistance 13 ? lies at right angles to a spatially uniform magnetic field. The loop carries an induced current of 340 mA.

----> At what rate is the magnetic field changing? dB/dt =__________ T/s

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2) A 520-turn solenoid is 27 cm long and 1.6 cm in diameter and carries 63 mA .

----> How much magnetic energy does it contain? U=_________ J

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3) In the figure, R = 2.0 k? and ?0 = 60 V . When the switch is closed, the current through the inductor rises to 10 mA in 22 ?s .

----> What is the inductance? L=_________ H

THANKS IN ADVANCE!!!

Explanation / Answer

here,

1)

area = 220 cm^2

area = 0.022 m^2

resistance , r = 13 ohm

current , I = 0.34 A

dB/dt * area/r = I

dB/dt * 0.022/13 = 0.34

dB/dt = 200.91 T/s

the rate at which the magnetic feild changing is 200.91 T/s

2)

number of turns , n = 520

length , l = 0.27 m

radius , r = 0.008 m

current , I = 0.063 A

L = u0*N^2*area/L

L = 1.26 * 10^-6 * 520^2 * pi*0.008^2 /0.27

L = 0.253 H

magnetic energy stored , E = 0.5 * L*I^2

E = 0.5 * 0.253*0.063^2

E = 5.02 * 10^-4 J

the magnetic energy stored is 5.02 * 10^-4 J

3)

R = 2000 ohm

e0 = 60 V

I0 = e0 /r = 60/2000 = 0.03 A

t = 22 * 10^-6 s

I = 0.01 A

let the inductance be L

I = I0 * ( 1- e^( - R*t/L))

0.01 = 0.03 * ( 1- e^( - 2000*22*10^-6 / L))

L= 0.11 H

the inductance is 0.11 H

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