Electromagnetic Induction Questions and Answers

NCERT Pg 261 12th part 1 for reducing resistance in tran sformer why we are using thick wires for high current low voltage windings alone Why we are not using for low curr ent high voltage windings

A particle having mass m charge q is projected with velocity vo along y axis in a region of uniform magnetic field Bo which is outward and perpendicular to the plane of the paper as shown in the figure The particle is continuously subjected to a frictional force which varies with velocity as F au where a is a constant Consequently the particle moves on a spiral path till it comes to rest at point P Find the x co ordinate of point P Take a 10 kg sec q 10 C4 Bo 1 T vo 1 m s m 5gm O O fe O O 106 O

Cx 10 A conducting wire frame is placed in magnetic field which is directed into the paper The magnetic field increasing at a constant rate The directions of induced current in wires AB and CD are LAT BE 3 A to B and D to C B to A and D to C X X X A B X X X X X X X X X X D 2 A to B and C to D 4 B to A and C to D

Two short magnet A and B of magnetic dipole moments M and M respectively are placed as shown The axis of A and the equatorial line of B are the same The magnetic force on one magnet due to the other is A M Ku M M 47 find k N B M

A conducting rod PQ of length L lies in the plane of the paper The rod is pivoted at the origin P and rotates with an angular velocity win the counterclockwise direction A uniform magnetic field Bexists along the positive z direction out of the plane of the paper The emf induced in the rod is A BoL with the end Q being positive with respect to P B C D BoL with the end P being positive with respect to Q BOL 2 with respect to P BOL 1 1 with the end Q being positive with the end P being positive

A transformer connected to a 120V power line has 200 turns in its primary winding and 50 turns in its secondary winding The second is connected to a 100 ohms light bulb How much current is drawn from the 120V power line

A rod of length is oriented along the unit vector 1 1 k It is rotating about one of its en 3 points with an angular velocity given by 1 The magnetic field in the region is given a B Bj Calculate the instantaneous EMF generated across the rod A B B 6 C Boco 3 B 4 D Bowl 12

The current I changes with time t in an inductor as shown in the given figure The potential difference e across the inductor is 5 1 3 t 2t 3t t 2t 3t 2 1 t 2t 3t hn b 4 t 2t 3t t 2t 3t 3

31 The amplitude of the magnetic field of a harmonic electromagnetic wave in vacuum is B 510 nt The amplitude of the electric field part of the wave is a 120 NC 1 c 510 NC 1 134 NC b d 153 NC 39 L

A rectangular loop with a sliding connector of length 1 1 0 m is situated in a uniform magnetic field B 2T perpendicular to the plane of loop Resistance of connector is r 20 Two resistances of 6 and 3 connected as shown in figure Find the external force required to keep the connector moving with a constant velocity 11 2m s

A cyclotron with a radius of 2 1 m is to accelerate deuterons H 2 to an energy of 10 MeV What frequency MHz is needed for the voltage between the dees Round your answer to 1 decimal place q 1 60 x 10 19 C pi 3 14 M H 2 2 014 amu 1 amu 1 66 x 10 27 kg 1 MeV 1 602 x 10 13 J

Q40 The self induced emf of a coil is 25 volts When the current in it is changed at uniform rate from 10 A to 25 A in 1 s the change in the energy of the inductance is O A 540 J O B 437 5 J O C 740 J O D 637 5 J

QA conducting wire xy of length and mass m is sliding without friction on vertical conduction rails ab and cd as shown in figure A uniform magnetic field B exists perpendicular to the plane of the rails x moves with a constant velocity of X R www 1 Y

A wire is sliding on two parallel conducting rails placed at a separation of 1m as shown in figure Magnetic field 2T exists in a direction perpendicular to rails What force is necessary to keep the wire moving with a constant velocity of 1 cm sec 1m ww 50 92 B 2T F v 1 cm s

A ballistic galvanometer a device to measure charge of resistance 2002 gives a full scale deflection for a charge of 640 C A coil of 300 turns and of 1000 resistance having an area of cross section A is to be constructed to measure magnetic field up to 1 6T by noting deflections in the galvanometer when the coil is suddenly removed from the field If the deflection produced should not exceed the full scale deflection the maximum area allowable for the coil is 200 mm 300 mm 400 mm 100 mm

Marking scheme 4 for all correct options 1 partial marks 0 if not attempted and 2 in all wrong cases 1 Several a particles of different speeds enter a uniform magnetic field confined into a cylindrical region If all the a particles enter the field radially and perpendicular to the axis of the cylindrical region what can you say about the time intervals that these particles spend in the magnetic field A Faster is the particle lesser is the time B Slower is the particle lesser is the time C Slower is the particle greater is the time D The time is same for all the particles B

40 In a coil of resistance 50 S2 the induced current developed by changing magnetic flux through it is shown in figure as a function of time The magnitude of change in flux through the coil is a 10 Wb c 32 Wb A I O S 0 2 t s t s b 20 Wb d 40 b

Find direction of induced current in secondary circuit for the following changes in primary circuit a Key is just closed b Some time after the closing of key CW 4 c Key is just opened 20 i 36 E e OLETO Ta 1 ACW R www ACW GA slur

A constant current I flows through a metal rod of length L and mass m that slides on frictionless rails as shown in the fig If the initial speed of the rod is v towards right and a magnetic field B acts vertically up the total distance travelled by the rod before my coming to a stop is where x xBiL Vo B

A metallic rod of length L 10 cm is hinged such that it is free to rotate about hinge point O in uniform magnetic field B 20 T as shown The value of induced emf in V across the rod when it becomes vertical after we cut string will be X X xx x XOX X X X X X X X X X X X X wwwwww X X X X X X X X X X X X X X X

27 Which one of the following is the property of a monochromatic plane electromagnetic wave in free space a Electric and magnetic fields have a phase difference of 7 2 b The energy contribution of both electric and magnetic fields are equal c The direction of propagation is in the direction of Bx E d The pressure exerted by the wave is the product of its speed and energy density The ratio of amplitude of magnetic field to the amplitude of electric field for an electromagnetic wave propagating in vacuum is equal to a the speed of light in vacuum b reciprocal of speed of light in vacuum c the ratio of magnetic permeability to the electric susceptibility of vacuum d unity 31 The amplitude of the magnetic field of a harmonic electromagnetic wave in vacuum is Bo 510 nT The amplitude of the electric field part of the wave is a 120 NC 1 b 134 NC d 153 NC c 510 NC 1 a 2 10 T c 6 10 T 32 A plane electromagnetic wave of frequency 50 MHz travels in free space along the x direction At a particular point in space and time E 6 3 V m At this point B is equal to a 8 33 108 KT c 4 1 10 T 33 An electromagnetic wave is propagating along x axis At x 1 m and t 10 s its electric vector E 6 V m then the magnitude of its magnetic vector is b 18 9 108 T d 2 1 10 T b 3x10 T d 5 10 T 34 Which of the following is not true for electromagnetic waves a They transport energy b They have momentum c d They travel at different speeds in air depending on their frequency They travel at different speeds in medium depending on their frequency A plane electromagnetic wave travels in free space c d along X direction If the value of B in tesla at a 37 The frequency of electromagnetic wave which is best particular point in space and time is 1 2 x 10 k the value of E in V m at that point is suitable to observe a particle of radius 3 x 10 cm is of the order of a 10 5 Hz a 1 2 b 3 6k c 1 2k d 3 6 c 10 Hz 35 The photon energy in units of eV for electromagnetic waves of wavelength 2 cm is a 2 5 x 10 19 c 3 2 x 10 16 b 5 2 x 10 d 6 2 x 10 5 36 The electric field of an electromagnetic wave travelling through vacuum is given by the equation E E sin kx ot The quantity that is independent of wavelength is a kto b A plane electromagnetic wave of frequency 25 MHz vacuum is travels in free space along x direction At a particular 38 The electric field part of an electromagnetic wave in point in space and time electric field E 6 3 V m The magnitude of magnetic field B at this point is a 1 2 x 10 6 T c 2 1 10 T b 1 2 x 10 T d 2 1 x 10 T b 10 4 Hz d 10 2 Hz 181 E 3 1 The wavelength of this part of electromagnetic wave is a 1 5 m b 2 m c 2 5 m d 3 5 m E 2 5 cos 2 E 0 The wave is 39 In the question number 38 the frequency corresponding to the given part of electromagnetic wave is a 5 4 x 10 Hz c 3 2 10 Hz rad 4x10 b 8 6 x 10 Hz d 4 8 x 10 Hz 40 In the question 38 the amplitude of magnetic field part of the given wave is a 2 10 T c 4 22 10 T 2x10 41 The electric field part of an electromagnetic wave in a medium is represented by E 0 1 x10 4 b 1 03 10 T d 5 x 10 T m rad

An alternating emf 100 cos 200t volt is connected in series to a resistance of 20 Q and inductance 100 mH The phase difference between current and emf in the circuit will be O EIN 2

In the figure as shown straight wire carries a constant current The direction of induced current in the rotating loop about an axis xx at the instant shown X X X Gros 1 is anticlockwise 2 is clockwise 3 there is no current in the loop 4 maybe clockwise or anticlockwise

2 33 A parallel plate capacitor is to be designed with a voltage rating 1 kV using a material of dielectri constant 3 and dielectric strength 10 Vm Dielectric strength is the maximum electric field material can tolerate without breakdown i e without starting to conduct electricity through partic ionisation For safety we should like the field never to exceed say 10 of the dielectric strength What minimum area of the plates is required to have a capacitance of 50 pF ns The dielectric strength of a material is defined as the maximum value of electric field which it can tolerate without breakdown If

27 A wire loop is placed in a region of time varying magnetic field which is oriented orthogonally function of time Assume the positive emf is the one which drives a current in the clockwise direction the plane of the loop as shown in the figure The graph shows the magnetic field variation as the and seen by the observer in the direction of B Which of the following graphs best represents the 17 induced emf as a function of time 1 1 1 BA 4 t 2 t t2 3 EA 1 12 t t 1 1 18 A c coi 1 A of 1 In 11 40 11

An emf induced in a secondary coil is 10000 V when the current breaks in the primary The mutual inductance is 5 H and the current reaches to zero in 104s in primary The maximum current in the primary before the break is 10 2 A 2 0 3 A 3 0 4 A 4 0 5 A

Two identical bulbs B and B each of resistance Ris connected in a circuit as shown in figure If at t to the switch S is opened then which of the following graph correctly represents the variation of current in the bulb B R L TIRANO R E B B R S

36 In the circuit shown in figure the jockey J is being pulled towards right so that the resistance in the circuit is increasing Its value at some instant is 5 22 The current in the circuit at this instant will be oooo 20V w J a 4 A b less than 4 A c more than 4 A d may be less than or more than 4 A depending on th value of L

10 V 4 zero To measure the field B between the poles of an electromagnet a small test loop of area 1 cm resistance 102 and 20 turns is pulled out of it A galvanometer shows that a total charge of 2 C passed through the loop The value of B is 2 0 01 Twaqool sdi 3 0 1 T 1 0 001 T 4 1 0 Toal

29 A horizontal wire is free to slide on the vertical rails of a conducting frame as shown in figure The wire has a mass m and length 1 Resistance of the circuit is R If a uniform X magnetic field B is directed perpendicular to the frame the terminal speed of the wire as it falls under the force of gravity is a B 1 c mgR mgR BI b mgl BR X X X K X X X X X X X X X X B X X X X X X X X X X www R X X X X X d mgR B212 X X

73 The entire network shown here has uniform wire having resistance per unit length 192 m It is placed in a uniform but time varying magnetic field B directed into the plane If magnetic field is increasing at a rate of 1T s the ratio 1 12 equals a 2 c 1 3 1m 1 m X 11 X 0 5 m b 4 d 1 6 X X 1 X X

3 2Rb 1 2R 2 R In a cylindrical region uniform magnetic field which is perpendicular to the plane of the figure is increasing with time and a conducting rod PQ is placed in the region If C is the centre of the circle then 2a R 1 P will be at higher potential than Q 2 Q will be at higher potential than P 3 Both P and Q will be at zero potential 4 No potential difference will be developed across the rod

he 40 A circuit consists of a resistance of 10 2 and a capacitance of 0 1 F If an alternating emf of 100 V 50 Hz is applied the current in the circuit is capac c Resistor inductor and capacitor d None of these e he a 3 14 mA c 1 51 mA b 6 28 MA d 7 36 mA

mtG Objective NCERT P 51 In a circuit L C and R are connected in series with an alternating voltage source of frequency The current leads the voltage by 45 The value of Cis 1 AU 2 UL R a b 1 nu 2nUL R c d 2nu 2nul R 1 2mv 2mul R 52 At resonance frequency the imped Aman A se Q F valu c In a in th A

Two concentric and coplanar circular coils have radii a and b a as shown in figure Resistance of the inner coil is R Current in the outer coil is increased from 0 to i then the total charge circulating the inner coil is 1 Hia 2Rb 2 Hoiab 2R 3 Hoi zb 2a R Haib 2 R

Consider a cylindrical region of uniform but time varying magnetic field Now conside a plane perpendicular to this field Top view of this cylindrical magnetic field on the plane is shown in the diagram which is a circular region of radius r 1m A particle of mass f kg charge 2C is projected with velocity of v 5m s tangential to the circle from point A This particle intersects another radial line OB at point B with velocity v If the magnetic field is increasing at the rate of 4T s then find the value of RAM X YATHE

Example 5 10 A shunt generator has an induced e m f of 254 volts When the generator loaded the terminal voltage is 240 volts Neglecting armature reaction find the load curre if the armature resistance is 0 04 ohm and the field circuit resistance is 24 ohms An

EXAMPLE 5 3 A 2000 V 3 phase star connected synchronous motor has an effective resistance and synchronous reactance of 0 2 2 and 2 2 2 per phase respectively The input is 800 kW at normal voltage and the induced line e m f is 2500 V Calculate the line current and power factor

current in the counterclockwise direction in A 5 Same as problem 4 except the coil A is made to rotate about a vertical axis No current flows in B if A is at rest The current in coil A when the current in B at 0 is counterclockwise and the coil A is as shown at this instant t 0 is 700 a constant current clockwise b varying current clockwise c varying current counterclockwise d constant current counterclockwise 8

3 A thin diamagnetic rod is placed vertically between the poles of an electromagnet When the current in the electromagnet is switiched on then the diamagnetic rod is pushed up out of the horizontal magnetic field Hence the rod gains gravitational potential energy The work required to do this comes from NEET 2018 1 The current source 2 The magnetic field 3 The lattice structure of the material of the rod 4 The iduced electric field due to the changing magnetic field A metallic rod of mass per unit length 0 5kg m is lying horizontally on a smooth inclined plane which makes an angle

ith energy conservation 6 An inductor of inductance 2 00 H is joined in series with a resistor of resistance 2002 and a battery of emf 2 00 V At t 10 ms find the current in the circuit b the power delivered by the battery the power dissipated in heating the resistor and the rate at 6 which energy is being stored in magnetic field Two coils 4 and 1 ree

88 A 10 V battery connected to 5 2 resistance coil having inductance 10 H through a switch drives a constant current in the circuit The switch is suddenly opened and the time taken to open it is 2 ms The average emf induced across the coil is a 4x 10 V b 2x 10 V c 2x 10 V d 1 x 10 V

99 A boy peddles a stationary bicycle the pedals f the bicycle are attached to a 200 turn coil of area 0 10 m The coil rotates at half a revolution per second and it is placed in a uniform magne field of 0 02 T perpendicular to the axis of rotat of the coil The maximum voltage generated in the coil is a 1 26 V 3 24 V c b 2 16 V d

c 3 24 V 100 An a c generator consists of a coil of 100 turns and cross sectional area of 3 m rotating at a constam angular speed of 60 radian sec in a uniform magnetic field of 0 04 T The resistance of the coil is 500 ohm What is the maximum power dissipation in the coil a 518 4 W c 259 2 W d 4 12 V b 1036 W d Zero

2 A loop made of straight edges has six corners at A 0 0 0 B L 0 0 C L L 0 D 0 L 0 E 0 L L and F 0 0 L A magnetic field B B i k T is present in the region The flux passing through the loop ABCDEFA in that order is a B L Wb c 2 B L 2 Wb b 2 B L Wb d 4 B L Wb

137 87 Two solenoids of equal number of turns have their lengths and the radii in the same ratio 1 2 The ratio of their self inductances will be a 1 2 c 1 1 88 A 10 V battery conn b 2 1 d 1 4

a 0 51s c 0 11s b 5 01 s d 2 01 s A 100 mH coil carries a current of 1 A Energy stored in its magnetic field is a 0 51 b 0 05J c 1J d 0 1J SA A to 10 A in 0 1 s the

The figure shows a conducting loop consisting of a half circle of radius r 0 1 m and three straight sections The half circle I in a uniform magnetic field that is directed out of the page and its magnitude is given by B 2 0t 2 0 with Bin Tesla and t seconds s The magnitude and direction of the emf induced around the loop at t 5s are a 3 14 mV counterclockwise O b 3 14 mv clockwise O c 3 14 V clockwise O d 3 14 V counterclockwise

d to The self inductance of an inductor coil having the cross section of the coil corresponding to a 100 turns is 20 mH The magnetic flux through current of 4 mA is a 2 x 10 Wb c 8 x 10 Wb b 4x 107 Wb d 8 x 105Wb ductance of a coil having 400 turns is

c 5 x 10 Wb d 2 x 10 Wb 65 A pair of adjacent coils has a mutual inductance of 2 5 H If the current in one coil changes from 0 to 40 A in 0 8 s then the change in flux linked with the other coil is a 100 Wb c 200 Wb b 120 Wb d 250 Wb 72