Q12 of 104 Page 306

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


More from this chapter

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10

A conducting square loop having edges of length 2.0 cm is rotated through 180° about a diagonal in 0.20 s. A magnetic field B exists in the region which is perpendicular to the loop in its initial position. If the average induced emf during the rotation is 20 mV, find the magnitude of the magnetic field

 11

A conducting loop of face-area A and resistance R is placed perpendicular to a magnetic field B. The loop is withdrawn completely from the field. Find the charge which flows through any cross-section of the wire in the process. Note that it is independent of the shape of the loop as well as the way it is withdrawn.

 13

Figure shown a metallic square frame of edge an in a vertical plane. A uniform magnetic field B exists in the space in a direction perpendicular to the plane of the figure. Two boys pull the opposite corners of the square to deform it into a rhombus. They start pulling the corners at t = 0 and displace the corners at a uniform speed u.

(a) Find the induced emf in the frame at the instant when the angles at these corners reduced to 60°.


(b) Find the induced current in the frame at this instant if the total resistance of the frame is R.


(c) Find the total charge which flows through a side of the frame by the time the square is deformed into a straight line.



 14

The north pole of a magnet is brought down along the axis of a horizontal circular coil (figure). As a result, the flux through the coil changes from 0.35 weber to 0.85 weber in an interval of half a second. Find the average emf induced during this period. Is the induced current clockwise or anticlockwise as you look into the coil from the side of the magnet?