A long solenoid of radius 2 cm has 100 turns/cm and carries a current of 5 A. A coil of radius 1 cm having 100 turns and a total resistance of 20 Ω is placed inside the solenoid coaxially. The coil is connected to a galvanometer. If the current in the solenoid is reversed in direction, find the charge flown through the galvanometer.


Given:


Radius of solenoid


No. of turns in the solenoid


Current in the solenoid


Radius of second coil


No. of turns in the coil


Resistance of the coil


We know that,


Magnetic field inside solenoid (B) is given by formula



Where,


n=no. of turns per unit length


i=current through solenoid


Magnetic flux(ϕ) through the coil is given by the formula




Where B=magnetic field intensity


A=area of cross section of the coil


θ =angle between area vector and magnetic field


magnetic field inside solenoid is perpendicular to the coil


initially flux through the coil is given by



When the current in the solenoid is reversed in direction of magnetic field gets reversed and flux through the coil now m=becomes




Now,


Average induced emf in time interval Δt is given by


…(i)


Where


are flux across the cross section at time intervals respectively


Putting these values in eqn.(i) we get



Current (i) through the coil of resistance R can be calculated as



Hence the charge (Q) passing through the coil in time Δt is



Putting the values of μ0, I, N, n π r’ and R in above eqn.



Therefore flowing through the galvanometer is


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