A circular coil enclosing an area of 200 cm^2 is made of 190 turns of copper wir

Question

A circular coil enclosing an area of 200 cm^2 is made of 190 turns of copper wire. The wire making up the coil has resistance of 7.0 Ohm, and the ends of the wire are connected to form a closed circuit. Initially, a 1.2-T uniform magnetic field points perpendicularly upward through the plane of the coil. The direction of the field then reverses so that the final magnetic field has a magnitude of 1.2 T and points downward through the coil. If the time required for the field to reverse directions is 0.50 s, what is the average current in the coil during that time? A technician wraps wire around a tube of length 35 cm having a diameter of 8.2 cm. When the windings are evenly spread over the full length of the tube, the result is a solenoid containing 550 turns of wire. Find the self-inductance of this solenoid. If the current in this solenoid increases at the rate of 3 A/s, what is the self-induced emf in the solenoid?

Explanation / Answer

given data
t=0.50s
A=200cm^2
N=190
R=7ohms
Bi=1.2T
Bt=1.2T
I=?

Faraday's Law:

E = -N *d(BA)/dt

I=E/R

I=( N*d(BA)/dt )/R

I=-(190*200*10^-4*(-1.2-1.2))/(0.50*7) = 2.606 A

18) given data

length l =35cm =0.35m
diameter =8.2 cm
radius =4.1cm =0.041m
N=550
dI/dt =3A/s

Using L = .AN²/l

L = (4*pi*10^-7*pi*0.041*0.041*550*550)/(0.35)

L=0.00573 H =5.73mH

Using E = (-) L.(i/t)

E = -0.00573*3 =-0.01719 V =17.19mV

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