Q24 of 104 Page 306

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.



Given:


Radius of circular coil


Magnetic field intensity


Angular speed of coil ω =


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




…(i)


As


Where ω =angular velocity of loop


Where θ is the angle between magnetic field and area vector of loop.


by faraday’s law of electromagnetic induction



Where


ϵ =emf produced


ϕ =flux of magnetic field


putting the value of eqn.(i) in above eqn. we get,


…(ii)


Since maximum value of is equal to 1



Putting the values of B, A and ω we get,


………. (iii)


Therefore maximum emf induced in the circular coil is


(b) from eqn.(ii) emf induced in the coil is given by



Average value of induced emf is given by formula



Where is the time taken by the coil to complete one revolution



Therefore, average induced emf is zero


(c). the average of squares of induced emf is given by the formula







Putting the values of B, A and ω we get


using eqn.(iii)


Therefore average of squares of emf produced is


More from this chapter

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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.

 25

Suppose the ends of the coil in the previous problem are connected to a resistance of 100 Ω. Neglecting the resistance of the coil, find the heat produced in the circuit in one minute.

 26

Figure shows a circular wheel of radius 10.0 cm whose upper half, shown dark in the figure, is made of iron and the lower half of wood. The two junctions are joined by an iron rod. A uniform magnetic field B of magnitude 2.00 × 10–4 T exists in the space above the central line as suggested by the figure. The wheel is set into pure rolling on the horizontal surface. If it takes 2.00 seconds for the iron part to come down and the wooden part to go up, find the average emf induced during this period.