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Chapter 6 Electromagnetic Induction Solutions

Question - 1 : - Predict the direction of induced current in the situations described bythe following Fig. 2(a) to (f).

Answer - 1 : -

(a) According to Lenz’s law south pole forms at q and northpole a to p. Therefore, induced current is from p to q.
(b) South pole develops atend q and at end x of the two coils as per Lenz’s law. Therefore, inducedcurrent is from q to p in coil PQ and x to y in coil
(c) The induced currentshould flow clockwise in the right loop (when seen from left) to oppose thecurrent in the left loop. Hence, induced current flows along yzx
(d) When rheostat isadjusted to increase the current, magnetic flux through the neighbouring coilincreases. As per Lenz’s law, induced current in the neighbouring coil shouldproduce magnetic flux in opposite direction to oppose the original magnetic flux.Hence, induced current flows along
(e) When circuit breaks,magnetic flux decreases. The induced current should flow along xry to increasethe magnetic flux.
(f) The magnetic fluxthreading the coil in the perpendicular direction is zero. Any change incurrent will not change this magnetic flux. Hence, no induced current is set upin the coil.

Question - 2 : - Use Lenz’s law to determine the direction ofinduced current in the situations described by Figure :
(a) A wire of irregularshape turning into a circular shape;
(b) A circular loop beingdeformed into a narrow straight wire.

Answer - 2 : -

(a) The flux linked with the loop increases in this case soflux produced by the induced current should decrease it i.e. the direction ofinduced current should produce magnetic field in a direction outwards the planeof the paper. The direction of current as per right hand thumb rule comes outto be along adcba. (i.e. anti­clockwise)

(b) In this case, the flux linked with the loop is decreasingso the direction of induced current is anticlockwise so as to oppose thedecrease in flux. Thus, direction of induced current is along a’d’c’b’.

Question - 3 : - A long solenoid with 15 turns per cm has a small loop of area 2.0 cm2 placedinside the solenoid normal to its axis. If the current carried by the solenoidchanges steadily from 2.0 A to 4.0 A in 0.1s, what is the induced e.m.f. in theloop while the current is
changing ?

Answer - 3 : -

Question - 4 : - A rectangular wire loop of sides 8 cm and 2 cm with a small cut ¡smoving out of a region of uniform magnetic field of magnitude O.3 T directednormal to the mop. What ¡s the e.m.f. developed across the cut if the velocityof the loop is 1 cm s-2 in a direction normal to the (a) longerside,
(b) shorter side of the loop ? For how long does the induced voltage last ineach case ?

Answer - 4 : - e = Blυ

Question - 5 : - A 1.0 m long metallic rod is rotated with an angular frequency of 400rad s_1 about an axis normal to the rod passing through its oneend. The other end of the rod is in contact with a circular metallic ring. Aconstant and uniform magnetic Field of 0.5 T parallel to the axis existseverywhere. Calculate the e.m.f. developed between the center and the ring.

Answer - 5 : -


Question - 6 : - A circular coil of radius 8.0 cm and 20 turns rotates about its verticaldiameter with an angular speed of 500 rad s_1 a uniformhorizontal magentic field of magnitude 3.0 x 10-2 T.Obtain the maximum and average emf induced in the coil. If the coil forms aclosed loop of resistance 10 Ω, calculate the maximum value of current in thecoil. Calculate the average power loss due to Joule heating. Where does thispower come from ?

Answer - 6 : -

(v) Source of power loss is the external rotorwhich provides the necessary torque to rotate the coil.

Question - 7 : - A horizontal straight wire 10 m long extending from east to west is fallingwith a speed of 5.0 ms-1, at right angles to the horizontalcomponent of the earth’s magnetic field,
0.30 x 10-4 Wb m-2.
(a) What is the instantaneous value of the e.m.f. induced in the wire ?
(b) What is the direction of the e.m.f. ?
(c) Which end of the wire is at the higher electrical potential ?

Answer - 7 : -


(b) Using Fleming’s Right hand rule, the direction of inducede.m.f. is from West to East.
(c) Since the rod will actas a source, the Western end will be at higher electrical potential.

Question - 8 : - Current in a circuit falls from 5.0 A to 0.0 As. If an average emf of200 V is induced, give an estimate of the self-inductance of the circuit.

Answer - 8 : -


Question - 9 : - A pair of adjacent coils has a mutual inductance of 1.5 H. If thecurrent in one coil changes from 0 to 20 A in 0.5 s, what is the change of fluxlinkage with the other coil ?

Answer - 9 : -

Using dΦ = Mdl, we get
dΦ= 1.5 X (20 – 0) = 30 Wb

Question - 10 : -

A jet plane is travelling towards west at aspeed of 1800 km/h. What is the voltage difference developed between the endsof the wing having a span of 25 m, if the Earth’s
magnetic field at the location has a magnitude of 5 x 10-4 Tand the dip angle is 30°? 

Answer - 10 : -


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