Electromagnetic Induction Questions and Answers

67 A short solenoid of radius a number of turns per unit length and length L is kept coaxially inside a 73 very long solenoid of radius b number of turns per unit length n What is the mutual inductance of the system a Hob n n L c Hona n n L b Horan n L d Honb n n L 74

c 9 54 H 71 Two conducting circular loops of radii R and are placed in the same plane with their centre coinciding If R R the mutual inductance y between them will be directly proportional to R R 72 A small cou a b R R d c 10 54 H H R d 2670

66 If number of turns in primary and secondary coils is increased to two times each the mutual inductance a becomes 4 times b becomes 2 times c becomes times d remains unchanged 67 A short solenoid of radius a number of turns per

49 A rod of length I rotates with a uniform ang velocity to about an axis passing through its mad point but normal to its length in a uniform magne field of induction B with its direction parallel to the axis of rotation The induced emf between the tw ends of the rod is BI a 2 BI c b zero d 2BF 53 In a o of 10 go 2 C

14 A long solenoid S has n turns per diameter a At the centre of this coil we place a smaller coil of N turns and diameter b b a If the current in the solenoid increases linearly with time then the emf will be induced in the smaller coil Which of the following is the correct graph showing le verses t if current varies as a function of m C a c e 0 b le d e 0

5 A 2 m long metallic rod rotates with an angular frequency of 200 rad s about an axis normal to the rod passing through its one end The other end of the rod is in contact with a circular metallic ring A constant magnetic field of 0 5 T parallel to the axis exists everywhere The emf developed between the centre and the ring is a 100 V c 300 V b 200 V d 400 V

a 0 02 A long solenoid with 10 turns per cm has a small loop of area 3 cm placed inside normal to the axis of the solenoid If the current carried by the solenoid changes steadily from 2 A to 4 A in 0 2 s what is the induced voltage in the loop while the current is changing a 4 2 x 10 V c 7 3 x 10 V b 2 8 x 10 V d 3 8 x 10 V Lid with length 20 cm area of 16 Acin 202 hor is re 0 3 at t 17 inc a c

b 3 A uniform magnetic field B points vertically up and is slowly changed in magnitude but not in direction The rate of change of the magnetic field is a A conducting ring of radius r and resistance R is held perpendicular to the magnetic field and is totally inside it The induced current in the ring is a zero b d 0 5 2rB c ra R Ta R

37 A conductor is moving with the velocity v in the magnetic field and induced current is I If the velocity of conductor becomes double the induced current will be a 0 51 c 21 b 1 51 d 2 51

3 In the shown figure the mutual inductance of two coils is M the coil II has resistance R and the se inductance L The current in the coil I varies according to the law i at where a is a constant and t time Find the current in coil II as function of time except M for the pair and L for the coil II ignore ar other effect of induction Loh Ma 24 ZIAL Ma CO Luw www B Coil I M 1 e Rt www Coil II C Ma Rt 1 e L Ma

132 21 A closed iron ring is held horizontally and a bar 26 magnet is dropped through the ring with its length along the axis of the ring The acceleration of the falling magnet is a equal to g b less than g c more than g d depends on the diameter of the ring and length of magnet CERVATION OF ENERGY

d it is given transl 35 When a wire loop is rotated in a magnetic field the direction of induced emf changes in every a one revolution c revolution 4 b revolution 2 d 2 revolution 41 42

While keeping area of cross section of a solenoid same the number of turns and length of solenoid one both doubled The self inductance of the coil will be 1 halved 2 3 times the original value 4 unaffected doubled

A line charge negligible mass with linear charge density A is wound around the circumference of an insulating uniform disc of mass M and radius R It is placed in uniform magnetic field Bo directed along its axis Initially it is held just above the rough ground and is free to rotate about its central axis Suddenly the field is switched off which causes the disc to rotate Now the disc is placed gently over rough horizontal surface If final angular 2 B R speed of disc is nM O 7 find the value of n Rough surface

The primary and secondary coils of a transformer have 50 and 1500 turns respectively If the magnetic flux linked with the primary coil is given by where is in weber is time in second and ois a constant the output voltage across the secondary coil is do 41 1 90 V 2 120 V 3 220 V 4 30 V

A ring of radius R is rotating about hinge O in vertical plane as shown Uniform magnetic field exist perpendicular to the plane of ring Induced emf between two points P and Q on same horizontal level is P 18 34 R BOR Boo R 2 Zero 2B0R

ho L A rectangular loop of sides 10 cm and 5 cm carrying 4 A a current I of 12 A is placed in different orientations sar as shown in the figure below fie The the the a c 1 3 2 BT If there is a uniform magnetic field of 0 3 T in the positive z direction in which orientations the loop would be in i stable equilibrium and ii unstable equilibrium a 2 and 4 respectively b 2 and 3 respectively c 1 and 2 respectively d 1 and 3 respectively 5 The ma ra co Os ma ai a c 6 So po po

A conducting disc of radius a and mass mis kept rotating with a constant angular speed in a horizontal plane about a vertical axis in a uniform vertical magnetic field B as shown in figure One metal contact B is made at the circumference of the disc and another contact B is made in such a way that its distance from centre is always a 2 If the switch Sis closed at t 0 then the value of current in the inductor at t In2 is 3Boa nR Value of n is ER L S X B X B ki a 2

A rectangular loop of sides a and b is placed in x y plane A uniform but time varying magnetic field of strength 20ti 10t i 50k is present in the region The magnitude of induced e m f in the loop at time t is 1 20 20t 3 20 t B 2 20 4 zero

A Zener diode of breakdown voltage Vz 10 V is used in the given circuit The current through the load resistor RL is 1 10 A 2 5 A 3 10 mA 4 5 mA 25 V 400 22 www V 10 V R 1 k

A coil of wire enclosing an area 100 cm is placed with its plane making an angle 60 with the magnetic field of strength 10 T What is the flux through the coil If magnetic field is reduced to zero in 10 s then find the induced emf

The two rails of a railway track insulated from each other and the ground are connected to a milivoltmeter the earth s magnetic field at the place is 0 4 G and the angle of dip is 30 and the rails are separated by 1m The reading of the of the voltmeter when a train travels at a speed of 180 km hr along the track is 0 010 mV 10 mV 100 mV 1mY

nducting loop having a capacitor is moving outward from the magnetic field Which plate of the capacitor will be positive X X X X X X X X X X X V a Plate A b Plate B c Plate A and Plate B both d None A B

In a region of uniform magnetic induction B 10 tesla a circular coil of radius 30 cm and resistance ohm is rotated about an axis that is perpendicular to the direction of B and which forms a diameter of the coil If the coil rotates at 200 rpm the amplitude of the alternating current induced in the coil is 1 4x mA 2 30 mA 3 6 mA 4 200 mA

Q 32 A single phase 50 Hz core type transformer has a core of a cross section area of 400 sq cm The permissible maximum flux density is 1 Wb m Calculate the number of turns per limb on the high and low voltage sides for a 3000 220v ratio N1 169 N2 15 N1 269 N2 13 N1 170 N2 13 N1 169 N2 13

Q 3 RMS value of emf per turn Form factor Average emf per turn Therefore RMS value of emf per turn per turn 1 11 x 4f om 4 44f om This is called the emf equation of transformer The average emf induced per turn in a transformer is given by 1 11f om O 0 5fm 4 44 f

Q 22 The transformer does this by linking together two or more electrical circuits using a common oscillating magnetic circuit which is produced by the transformer itself A transformer operates on the principles of electromagnetic induction in the form of Mutual Induction According to the figure below what is the amount of the secondary voltage of the transformer Np 500 loops Vp 220 Volt Vs 23 Volt Vs H 2200 Volt Vs 2000 Volt Vs 2400 Volt Vs 2300 Volt Ns 5000 loops Output voltage

An inductor of inductance L 400 mH and resistors of R 2 and R 22 are connected to a battery emf 12 V as shown in the figure The internal resistance of the battery is negligible The switch S is closed at t 0 The potential drop across L as a function of time is E 5t Tr www R Weeee R

35 Two transformers are arranged as shown The primary of the transformer to the left which has N number of turns is connected to a 120 V ac supply The secondary of this transformer which has 2N number of turns is connected to the primary arm of the transformer to the right which also has 2N number of turns The secondary of the transformer to the right has N number of turns and there is a bulb in the circuit If the resistance of the bulb is 60 92 what is the current passing through the wire which connects the two transformers 20 V ac N turns A 0 25 A B 0 5 A C 1 A 2N turns bulb N turns

Q 37 A single phase 50 Hz core type transformer has a core of a cross section area of 400 sq cm The permissible maximum flux density is 1 Wb m Calculate the number of turns per limb on the high and low voltage sides for a 3000 220v ratio N1 269 N2 13 N1 170 N2 13 N1 169 N2 13 N1 169 N2 15

A solenoid have the self inductance 2H If length of the solenoid is doubled having turn density and area constant then new self inductance is 1 4H 2 1H 3 8H A solenoid wound over a rectangular frame If all the linear dimanci 4 0 5 H E

2 16 0 A s 3 1 6 A s 4 Two coils A and B having turns 300 and 600 respectively are placed near each other on passing a current of 3 0 ampere in A the flux linked with A is 1 2 x 104 weber and with B it is 9 0 10 weber The mutual inductance of the system is 1 2 x 10 5 H 2 3 x 10 5 H 4 6 x 10 5 H utual inductance is M then the value of induced 3 4 x 105 H

A parallel plate capacitor with air between the plates has a capacitance of 8 pF The separation between the plates is now reduced by half and the space between them is filled with a medium of dielectric constant 5 Calculate the value of the capacitance of the CBSE AI 2006 Delhi 2005 capacitor in the second case

A coil of N turns A area is placed in uniform transverse magnetic field B If it is turn through 180 abor its one of the diameter in 2 seconds Find rate of change of magnetic flux through the coil G A square cube of side a is placed in uniform magnetic field B Find magnetic flux through H

A circular conducting coil of radius ro having resistance R is placed in a time varying transverse uniform magnetic field B 4t as shown in the figure The current in the coil at time t 2 s is consider all quantities are in SI units B X X X X X X X X X X X X x x x x x x x x X X X X X X X xxxxx x X X X X X X X X X x x x x x xxxx xx XXXXXXX X X X X X X X X X X X X X X X X X X X X X 16 r R 4 Tur R 8 Tur R

Moving Charges and Magnetism In 8 cm long wire carrying a current of 10 A is olenoid perpendicular to it

Diagram shows two parallel and coaxial loops smaller loop is of radius r Magnetic field due to current i in larger loop radius R r is nearly constant throught the smaller loop Seperation between the loops is x R then mutual inductance between the loops ft 3 R 2x3 4 R r 6x3 O HR 4x3 Ho R r 2x3 Marks 4 1 L

Two coils are placed close to each other The mutual inductance of the pair of coils depends upon Question Type Single Correct Type 1 the rates at which currents are changing in the two coils 2 3 4 relative position and orientation of the two coils the materials of the wires of the coils the currents in the two coils

A electromagnetic wave wave going through a medium is given by E Eosin kx wt B Bosin kx wt then A Ek Bow B If Electric is in Z direction them magnetic field should be in y direction C Both A and B are correct D Only A is correct

A uniform rod AB of mass M is attached to a hinge at one end A and released from rest from t horizontal position The rod rotates about A and when it reaches the vertical position the r strikes a sphere of mass m and radius r initially at rest on the smooth horizontal surface as show in the adjacent figure The impact is along the horizontal direction and perfectly elastic If at th moment of impact the lowest end of the rod is very close to the smooth horizontal surface Aft the impact the sphere moves along the horizontal and the rod subsequently rises to a maximu of 60 with the vertical Choose the correct statement s form the following taking into accou m 6 2 the information given above The length of the rod equals 2r r 10 Initial postion m final position A a A The ratio M m is 3 2 B The ratio m M is 2 3 C The speed of the sphere just after collision is 6 m s D The speed of the sphere just after collision is 3 m s m

2 2 104T 4 4 x 10 T 3 2 10 T A wire has length 1 m radius 2mm and 20000 Find its self inductance 1 2 mH 2 1mH 3 3 mH 4 4 mH Q A

0 M 4 In a gravity free region a T shape rigid insulating frame is rotating in its plane about the end of the central bar of length 1 with a constant angular velocity A strong uniform and static magnetic field of induction B exists everywhere pointing into the plane of the frame Two identical beads P and P each of mass m and charge q can slide without friction on the frame a Find the equilibrium position of the beads relative to the frame b What can you say about the equilibrium positions if sign of charge 13 of one of the beads is reversed tane 9 13 98m q

A uniform conducting rod of length is moving with spee Vo in a uniform transverse magnetic field Bo as shown in figure The emf developed across the two ends of the ro will be x x XAX Bo 30 X B X X X X Bolvo and A is at higher potential Bolvo and A is at higher potential 2 Bolvo and B is at higher potential Bolvo and B is at higher potential 2

A uniform conducting rod of length is moving with speed vo in a uniform transverse magnetic field Bo as shown in figure The emf developed across the two ends of the rod will be X X X A Bo X X X X X X X xx X B X 30 X X X XX Bolvo and A is at higher potential Bolvo and A is at higher potential 2 Bolvo and B is at higher potential Bovo and B is at higher potential 2

A flexible conducting loop is in the shape of a circle with radius r The loop is in a uniform magnetic field perpendicular to the plane of the loop To sustain a constant emf in the loop the radius r must vary with time according r 1 x t r t x t O r t xt r should be constant

0 a constant force F start acting o on smooth horizontal surface in a region where transverse uniform magnetic field t a at its mid point as shown Potential difference between ends the rod Vp Vo at any time t is X X X 3 X A X X BFet 2m 5BFft X X X X X X X x 30 X X X 2 4 X Q X X X X X X X BF lt 4m 7BFlt X X x x X X

In a cylindrical region of radius R there exists a time varying magnetic field B such that dB k 0 A charged particle having charge q is placed at the point P at a distance d R fro dt its centre O Now the particle is moved in the direction perpendicular to OP see figure by an external agent upto infinity so that there is no gain in kinetic energy of the charged particle Choos the correct statement s A Work done by external agent is B Work done by external agent is C Work done by external agent is D Work done by external agent is 97R 4 k if d 2R qaR 8 k if d 4R 97R 4 k if d 4R q R 4 k if d 6R

SolveLancer Test Consider a coil of 350 turns having cross section area 1 4 m The coil is placed in a region where magnetic field changes from 0 50 Wb m to 0 98 Wb m uniformly in 0 08 seconds The induced emf is applied in a wire of 200 ohm The value of current flowing in the wire is SolveLancer Test a 33 A b 27 3 A c 14 7 A d 7 323 A

In order to use use a 12 V lamp on a 230 V power line a transformer is applied a Give the number of turns in the secondary coil if the primary coil contains 1000 turns 10 points b The mutual induction coefficient of the transformer is M 0 1 H How large is the self induction coefficient L of the 10 points primary coil

In a Faraday disc dynamo a metal disc of radius R rotates with an angular velocity w about an axis perpendicular to the plane of the disc and passing through its center The disc is placed in a magnetic field B acting perpendicular to the plane of the disc Determine the induced emf between the rim and the axis of the disc