Q22 of 104 Page 306

A closed coil having 100turns is rotated in a uniform magnetic field B = 4.0 × 10–4 T about a diameter which is perpendicular to the field. The angular velocity of rotation is 300 revolutions per minute. The area of the coil is 25 cm2 and its resistance is 4.0 Ω. Find

(a) the average emf developed in half a turn from a position where the coil is perpendicular to the magnetic field,


(b) the average emf in a full turn and


(c) the net charge displaced in part (a).



Given:


No. of turns in the coil


Magnetic field intensity


Angular velocity of rotation


Area of the coil


Resistance of the coil


Magnetic flux through the circular coil ϕ can be given by formula



…. (i)


Where B=magnetic field intensity


A=area of cross section


N=no. of turns in the coil


θ =angle between area vector and magnetic field


(a) Initially, angle between area vector and magnetic field is 0°


Therefore, initial flux through the coil is



When it is rotated by 180° flux passing through the coil is given by



Average induced emf in time interval Δt is given by


…(i)


Where


are flux across the cross section at time intervals respectively.


Average induced emf is then given by


……(ii)


Now,


Angular velocity of coil


Time taken to complete half revolution i.e. rotate by π radian



Putting the values of N, B, A and Δt in eqn.(ii)



Therefore average emf induced in the coil in half a turn is


(b) In a full term coil returns to its original position



And hence emf induce in the coil using eqn.(ii) is



Therefore, average emf induced in full turn in the coil is zero


(c) Emf induced in the coil in part (a) is



Hence the current i flowing through the coil of resistance R is



So the charge displaced in time interval Δt =0.1s is



Therefore net charge displaced in part (a) is


More from this chapter

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20

Figure shows a circular coil of N turns and radius a, connected to a battery of emf ϵ through a rheostat. The rheostat has a total length L and resistance R. The resistance of the coil is r. A small circular loop of radius a’ and resistance r’ is placed coaxially with the coil. The center of the loop is at a distance x from the center of the coil. In the beginning, the sliding contact of the rheostat is at the left end and then onwards it is moved towards right at a constant speed v. Find the emf induced in the small circular loop at the instant

(a) the contact begins to slide and


(b) it has slid through half the length of the rheostat.



 21

A circular coil of radius 2.00 cm has 50 turns. A uniform magnetic field B = 0.200 T exists in the space in a direction parallel to the axis of the loop. The coil is now rotated about a diameter through an angle of 60.0°. The operation takes 0.100s.

(a) Find the average emf induced in the coil.


(b) If the coil is a closed one (with the two ends joined together) and has a resistance of 4.00 Ω, calculate the net charge crossing a cross-section of the wire of the coil.


 23

A coil of radius 10 cm and resistance 40 Ω has 1000 turns. It is placed with its plane vertical and its axis parallel to the magnetic meridian. The coil is connected to a galvanometer and is rotated about the vertical diameter through an angle of 180°. Find the charge which flows through the galvanometer if the horizontal component of the earth’s magnetic field is BH = 3.0 × 10–5 T.

 24

A circular coil of one turn of radius 5.0 cm is rotated about a diameter with a constant angular speed B = 0.010 T exists in a direction perpendicular to the axis or rotation. Find

(a) the maximum emf induced,


(b) the average emf induced in the coil over a long period and


(c) the average of the squares of emf induced over a long period.