Q21 of 104 Page 306

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.



Given:


Radius of coil


No. of turns in the coil


Magnetic field intensity


We know that,


Flux (ϕ) of magnetic field (B) through the loop of cross section area A in the magnetic field is given by




Where N=no. of turns in the coil


Since magnetic field is perpendicular to the loop the flux becomes



Initial flux through the coil is given by



After 0.1 s the coil is rotated through an angle of 60° =θ


Finally, the flux through the coil becomes



Average induced emf in time interval Δt is given by


…(i)


Where


are flux across the cross section at time intervals respectively.


Using eqn.(i) emf induced in the coil is given by



Putting the values of N, B, A and Δt in above eqn. we get



Therefore average emf induced in the coil is


(b) the current through the coil (i) is calculated using formula



Hence the charge(Q) crossing the cross-section of the wire in time interval Δt is



Putting the values of ϵ, R and Δt we get,



Therefore charge crossing cross-section of the wire in the coil is


More from this chapter

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19

The magnetic field in the cylindrical region shown in figure increases at a constant rate of 20.0 mT/s. Each side of the square loop abcd and defa has a length of 1.00 cm and a resistance of 4.00 Ω. Find the current (magnitude and since) in the wire ad if

(a) the switch S1 is closed but S2 is open,


(b) S1 is open but S2 is closed,


(c) both S1 and S2 are open and


(d) both S1 and S2 are closed.



 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.



 22

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).


 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.