A solenoid of length 60 cm has 10,000 loops, each of radius 10 cm and is connect

Question

A solenoid of length 60 cm has 10,000 loops, each of radius 10 cm and is connected to a battery that delivers a 5A current at some time t. If the solenoid is placed perpendicular to the page, the current is seen to be counter clockwise. A smaller loop or radius 2.5 and resistance 5 m ohms is placed in the solenoid with its plane parallel to the solenoid's loops.

A) assuming the loop stays fully inside the solenoid and the current in the solenoid is constant, which actions induce a current in the loop?

*moving the loop along the solenoid's axis (perpendicular to the page)

*moving the loop in the plane of the page

*rotating the loop about one of its diameters

rotating the loop about solenoids axis

B) for this question, assume the loop is back at the center of the solenoid, with its plane forming a 10 degree angle with the plane of the page. You change the current in the solenoid and observe that there is a 3mA current with a counter clockwise direction induced in the loop. Was the current in the solenoid increased or decreased? At what raite was it changed?

Explanation / Answer

A) rotating the loop about one of its diameters

beacsue in this only case magnetic flux through the loop changes and induced current floes in the loop.

B) The current in the solenoid decreased.

N = 10000 loops

L = 60 cm = 0.6 m

cross sectional area of loop, A = pi*r^2

= pi*0.025^2

= 1.96*10^-3 m^2

magnetic field produced by solenoid, B = mue*N*I/L

induced emf in the loop = induced current*R

= 3*10^-3*5*10^-3

= 15*10^-6 volts

induced emf = A*cos(theta)*dB/dt

induced emf = A*cos(theta)(mue*N/L)*dI/dt

==> dI/dt = induced emf*L/(A*cos(theta)*mue*N)

= 15*10^-6*0.6/(1.96*10^-3*cos(10)*4*pi*10^-7*10000)

= 0.37 A/s

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