A long solenoid of radius a, carrying n turns per unit length, is looped by a wi

Question

A long solenoid of radius a, carrying n turns per unit length, is looped by a wire with resistance R, as shown below. If the current in the solenoid is increasing at a constant rate (dI/dt = k), what current flows in the loop, and which way (left or right) does it pass through the resistor? If the current I in the solenoid is constant but the solenoid is pulled out of the loop and reinserted in the opposite direction, what total charge passes through the resistor? [Hint: Consider the total difference in flux between the two configurations]

Explanation / Answer

magnetic field due to solonoid is given by B = uo n i

where n = N/l

so

B = uo Ni/L

accoridng to lenz law indcued current always opposes the cause of its motion

so

here current moves to the left

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also induced emf is defiend as the rate of change of magnetic flux

in mathematical form,

induced emf e = NAdB/dt or NABW or NA dB/dt cos theta

where A = area

N = no. of tunrs

W = angular frequency

dB/dt = rate of change of magnetic field

induced current i = e/R

Where R = resisatnce

so iR = e = NAdB/dt

i dt R = N( pi a^2) (uo NI/L)

since charge q = it

here charge Q = N^2 pi a^2 uo I/LR

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