MEEC 12 Magnetic Effect of Electric Current · 2020. 4. 6. · MEEC 1 12 Magnetic Effect of...

1MEEC

12 Magnetic Effect of Electric Current

Syllabus

12.0 Introduction

12.1 Biot-Savart's law (Laplace law)

12.2 Right hand thumb rule

12.3 Magnetic induction at the centre

of circular coil carrying current

12.4 Magnetic induction at a point

along axis of coil carrying

current

12.5 Force acting on a current carrying

conductor in a magnetic field

12.6 Fleming's left hand rule

12.7 Force between two infinitely long

current carrying parallel

conductors

12.8 Definition of Ampere

12.9 Torque on a current loop in

magnetic field

Formulae

1. Biot-Savart's law :

i. 20

r

sinId.

4dB

l

ii.

30

r

rdI.

4dB

l (in vector form)

2. Magnetic induction at a point due to straight

conductor carrying current :

a2

IB 0

3. Magnetic field at the centre of the circular

coil :

i.r2

IB 0 (for single turn)

ii.r2

nIB 0 (for n turns)

4. Magnetic induction at a point along the axis

of a coil carrying current :

i. 2/322

20

)xa(2

IaB

(for one turn)

ii. 2/322

20

)xa(2

nIaB

(for n turns)

iii.a2

nIB 0 (at the centre of coil)

iv. 3

20

x2

nIaB

(at the point far away from centre

of coil)5. Force on a moving charge :

F = qvB sin .6. Force acting on a conductor carrying

current:

F = I/B sin

A is simply a device that produces currentfrom mechanical energy. Whenever, the amount of magnetic flux linked with a coil (armature) changes,an e.m.f. is induced in the coil giving rise to inducedcurrent.Modern generators produce power of the order of 500 MW i.e. we can light up 5 million bulbs of 100 W each simultaneousl.

generator

Generator

Axle rotated mechanically

Armature

Slip ring

Brush

l

b

a

l

l

DGT Group - Tuitions (Feed Concepts) XIth – XIIth | JEE | CET | NEET | Call : 9920154035 / 8169861448

DGT MH –CET 11th PHYSICS Study Material 1

2MEEC

7. Lorentz force:

BvqEqF

8. Force on length l of the wire :

a2

IIF 210

l

9. Force per unit length between two infinitely

long current carrying conductor :

a2

IIF 210

l

10. Torque on a current loop :

i. = IAB sin .

ii. = MB sin

iii.

BM (in vector form)

11. Magnetic moment of current carrying loop :

i. M = IA (For single turn)

ii. M = nIA (For n turns)

Notes

1.

2. A circular coil carrying current behaves as amagnetic dipole.

3. For a point on the axis of a circular coil carryingcurrent, magnetic field is maximum at the centreof the coil.

4. The magnetic field produced due to currentthrough a conductor is always in a planeperpendicular to the plane of the conductor.

5. If a straight current carrying wire is placed alongthe axis of a current carrying coil then it will notexperience magnetic force because magnetic fieldproduced by the coil is parallel to the wire.

6. Lorentz force is maximum, when the chargedparticle moves at right angles to the field. The

force is zero when the charged particle is at restor moving parallel or antiparallel to the field.

7. Torque on current loop in a magnetic field is givenby,

BM = MB sin = nIAB sin .

Mindbenders

1. Electric force is an absolute concept whilemagnetic force is a relative concept for anobserver. This is because motion is relativeconcept. Hence the magnetic field due to motionof charge is also relative. For example, when acharge is moving relative to you, there is a definitemagnetic field associated with the moving charge.But if you move along with the charge and thereis no relative motion between charge and you,there is no magnteic field associated with thecharge.

2. The net magnetic force on a current loop in auniform magnetic field is zero but torque may ormay not be zero.

3. The net magnetic force on a current loop in anon-uniform magnetic field is not zero but torquemay or may not be zero.

4. When a current loop is in the position ofequilibrium in a uniform magnetic field, then thenet magnetic force as well as torque on currentloop are zero.

5. Torque on the coil is maximum, when coil issuspended in a radial magnetic field.

6. The force on a wire carrying current of any shapein a uniform magnetic field is independent of itsshape but depends on the vector length joiningthe initial and final points of the current carryingwire.

Shortcuts

1. The magnetic Lorentz force does no work on thecharge, as it always acts perpendicular to thedirection of motion of charge.

2. If a current carrying circular loop (n = 1) is turnedinto a coil having n identical turns then magneticfield at the centre of the coil becomes n2 timesthe previous field i.e. B

(n turn) = n2 B

(single turn).

3. The value of magnetic field induction at a point,on the centre of separation of two linear parallelconductors carrying equal currents in the samedirection is zero.

Condition Result

charge is stationary only electric field

charge is moving with electric field and

uniform velocity magnetic field

charge is moving with electric field,accelerated motion magnetic field and

electromagneticradiations



3MEEC

Multiple Choice Questions

Classical Thinking

12.0 Introduction

1. The phenomenon in which magnetic field isproduced in the space near a conductor carryingcurrent is called ________ .a) thermionic effectb) photoelectric effectc) heating effectd) magnetic effect of electric current

2. The magnitude of magnetic strength at any pointin magnetic field is ________a) electric fluxb) electric flux per unit areac) magnetic fluxd) magnetic flux per unit area

3. Which of the following is NOT the unit ofmagnetic induction ?a) gauss b) weber/m2

c) maxwell d) tesla4. The dimensions of magnetic induction are

a) [M–1L–2T0A1] b) [M1L0T–2A–2]c) [M1L0T–2A–1] d) [M1L0T–1A–1]

12.1 Biot-Savart's law (Laplace's law)

5. The magnitude of magnetic induction at a pointdue to a small current carrying conductor isa) direclty proportional to currentb) directly proportional to square of distance of

point from centre of elementc) inversely proportional to the distance of point

from centre of elementd) inversely proportional to length of conductor

6. The value of magnetic induction will be minimumat a point due to a small current carryingconductor when angle between element and linejoining point and centre of element isa) 900 b) 1800

c) 00 d) both 'b' and 'c'7. The magnitude of magnetic induction at a distance

4 cm due to straight conductor carrying a currentof 10 A isa) 5 × 10–6 Wb/m2 b) 5 × 10–5 N/Amc) 5 × 10–5 gausss d) 5 × 10–6 tesla

8. The magnetic field produced around a straightline wire when current flows through it isa) parallel to the wireb) perpendicular to the wirec) in the form of concentric circled) parabolic line

9. A tangent to a point on the magnetic lines of forcegives us the direction of ______a) magnetic flux density

b) magnetic inductionc) magnetic fluxd) magnetic dipole

10. The dimension and SI unit of permeability of freespace (

0) are

a) [M1L2T–2A–2], Wb/Am2

b) [M1L2T–2A–1], Wb/Am2

c) [M1L1T–2A–3], Wb/Am2

d) [M1L1T–2A–2], Wb/Am2

11. In vector form the magnetic induction dB at apoint of distance r from centre of element oflength dl is given as

a)

20

r

sinId

4dB

l

b)

20

r

rdI

4dB

l

c)

30

r

drI

4dB

l

d)

30

r

rdI

4dB

l

12.2 Right hand thumb rule

12. The direction of magnetic field produced arounda long straight conductor is given bya) right hand thumb ruleb) left hand thumb rulec) right hand screw ruled) both 'a' and 'c'

13. According to right hand thumb rule, if current isdirected in upward direction then the direction ofmagnetic induction is _______.a) anticlockwiseb) clockwisec) same as currentd) opposite to that of current

12.3 Magnetic induction at the centre of circular

coil carrying current

14. A current carrying coil is equivalent toa) electric dipole b) magnetic dipolec) magnetic moment d) both 'a' and 'b'

15. If the current flowing in a circular loop is inanticlockwise direction then the magnetic inductionwill bea) along the direction of currentb) opposite to the direction of currentc) directed outwardsd) directed inwards



4MEEC

16. If the current flowing in a circular loop is inclockwise direction, then the magnetic inductionwill bea) along the direction of currentb) perpendicular to plane of coilc) directed inwardsd) both 'b' and 'c'

17. The magnetic induction at centre of loop due tocurrent flowing through small element 'dl' is given

as

20

r

sinId

4db

l where is

a) 00 b) 1800

c) 900 d) 600

18. The magnetic induction at the centre of a coilmade from a wire of length 22 cm carrying acurrent of 0.5 A isa) 8 × 10–6 Wb/m2 b) 0.9 × 10–6 Wb/m2

c) 9 × 10–6 Wb/m2 d) 0.8 × 10–6 Wb/m2

12.4 Magnetic induction at a point along axis of


19. A circular coil having 50 turns each of radius0.05m carries a current of 1 A. The magnitudeof magnetic induction at a point 0.2 m from itscentre on its axis isa) 9 × 10–6 gauss b) 9 × 10–5 N/Amc) 9 × 10–4 T d) 9 × 10–6 Wb/m2

12.5 Force acting on a current carrying conductor

in a magnetic field

20. A magnetic fielda) always exerts a force on a charged particleb) never exerts a force on a charged particlec) exerts a force, if the charged particle is moving

across the magnetic field linesd) exerts a force, if the charged particle is moving

along the magnetic field lines21. A straight conductor carrying a current does not

experience a force when it isa) parallel to magnetic fieldb) perpendicular to magnetic fieldc) antiparallel to magnetic fieldd) both 'a' and 'c'

22. The C.G.S. units of magnetic induction area) dyne emu–1 cm–1 b) oerstedc) gauss d) all of these

23. The force acting on a particle of charge q movingin a uniform magnetic field with velocity 'v' is

a) parallel to both

v and B

b) perpendicular to both

v and B

c) parallel to

v and perpendicular to B

d) perpendicular to

v and parallel to B24. When a particle carrying a charge of 200 C

moves at an angle 300 to a uniform magnetic fieldof induction 5 × 10–5 Wb/m2 with a speed of2 × 105 m/s. The force acting on the particle isa) 5 × 10–3 N b) 10–3 Nc) 2 × 10–3 N d) 10–4 N

25. A force of 1.732 × 10–2 N acts on a particle ofcharge q moving with a velocity 1/1000th of thevelocity of light in a magnetic field of induction

25 m/Wb103

2 and perpendicular to the field

then q isa) 5000 C b) 5000 Cc) 500 C d) 500 C

26. The magnetic force acting on a conductor of lengthl carrying a current I placed in field of strength Bis given as

a)

lBIF b)

BIF l

c)

BIF l d)

lBIF

27. A conductor of length 1 m and carrying currentof 1 A is placed at an angle 450 to the magneticfield of 1 oersted. The force acting on conductoris

a) N2

10 4

b) N3

10 4

c) N3

10 2

d) N2

10 2

28. The maximum force acting on a straight conductorof length 15 cm, placed in magnetic field ofinduction 5 × 10–5 N/A m is 3 × 10–4 N then thecurrent flowing in conductor isa) 40 mA b) 4 × 10–3 Ac) 400 mA d) 40 A

29. The force acting on a charge 'q' in both electricand magnetic field, simultaneousy is

a)

vBqEqF

b)

BvqEqF

c)

BvqEqF

d)

BvqEqF



5MEEC


30. In Fleming's left hand rule, the thumb points inthe direction of ______ .a) currentb) magnetic fieldc) motion of conductord) force acting on conductor

31. For a given conductor the directions of currentand magnetic induction are shown in the followingfigure. Which of the following represents directionof force ?

(1)

(2)

(3) (4)

I

B

a) 1 b) 2c) 3 d) 4

12.7 Force between the infinitely long current

carrying parallel conductors

32. When the current flowing in two long straightconductors parallel to each other and separatedby a finite distance are flowing in oppositedirection, the force that exists between theconductors isa) force of attractionb) force of repulsionc) force due to torqued) force due to friction

33. Two long straight conductors of length 1 m eachseparated by a distance of half metre and carryingcurrents of 200 A and 50 A respectively in oppositedirections. Then the force of attraction isa) 4 × 10–4 N b) 4 × 10–3 Nc) 2 × 10–3 N d) zero

34. Two long and stretched conductors, placedparallel to each other are separated by 10 cm,carrying current of 2 A and 4 A respectively inopposite direction. The force per unit lengthexerted by each conductor on the othera) 16 × 10–5 N/m b) 1.6 × 10–5 N/mc) 32 × 10–5 N/m d) 3.2 × 10–5 N/m

35. Two long parallel wires are at a distance of 4 cm.They carry currents I and 3I in same direction.Where will the field produced by both wires bezero from current I ?a) 0.02 cm b) 0.01 cmc) 1 cm d) 3 cm


36. The quantity of charge that flows through a givencross section in one second, when there is a steadycurrent of one ampere isa) 1.6 × 10–9 coulombb) 6.023 × 1023 coulombc) 1 coulombd) zero

37. The force of attraction between two long parallelconductors 1 metre apart carrying unit amperecurrent in same direction isa) 2 × 10–7 N/m b) 10–7 N/mc) 10–5 N/m d) 0.5 × 10–6 N/m

12.9 Torque on a current loop in magnetic field

38. A rectangular current carrying loop in a uniformmagnetic field experiences ______a) forceb) torquec) both 'a' and 'b'd) pressure

39. If the net magnetic force acting on a loop is zerothena) no torque acts on loopb) loop performs translational motionc) torque may or may not act on the loopd) both 'a' and 'b'

40. Maximum torque acting on a rectangular coil ofn turns and area A coinciding with the magneticfield B isa) – nIAB b) nIAB

c) zero d) nIAB2

1

41. A square coil of side 10 cm consists of 20 turnsand carries a current of 12 A. The coil issuspended vertically and the normal to the planemakes an angle of 300 with the direction ofuniform magnetic field of 0.8 T. The torque actingon the coil isa) 0.69 N m b) 0.96 N mc) 0.096 N m d) 0.069 N m

42. The magnetic moment of a square coil having 5turns, each side measuring 4 cm and carrying acurrent of unit ampere isa) 20 × 10–3 Am2 b) 8 × 10–3 Am2

c) 8 Am2 d) 16 × 10–3 Am2

Miscellaneous

43. Which of the following relation is correct ?a) 1 tesla = 10–4 gaussb) 1 gauss = 104 Wb/m2

c) 1 gauss = 104 N/Amd) 1 Wb/m2 = 1 N/Am



6MEEC

44. The magnetic induction at the centre of circularcoil carrying current of 1.4 A is 1.76 × 10–6 N/Amthen the circumference of the loop isa) 0.5 m b) 3.14 mc) 0.57 m d) 6.28 m

45. A long straight wire carrying a current of 50 A.An electron moving at 107 m/s is 5 cm away fromthe wire. The force acting on electron if its velocityis directed towards the wire will bea) 1.6 × 10–6 N b) 3.2 × 10–16 Nc) 4.8 × 10–16 N d) 1.8 × 10–16 N

46. The magnitude of magnetic induction due to astraight long conductor at a distance 10 cm fromconductor is 1.33 × 10–4 Wb/m2. If electrons flowthrough the conductor, the number of particlesflowing per second isa) 3.9 × 1021 b) 4.1 × 1020

c) 4.4 × 1020 d) 3.9 × 1020

Critical Thinking

12.0 Introduction

1. A current carrying wire in the neighbourhoodproducesa) no fieldb) electric field onlyc) magnetic field onlyd) electric and magnetic field

12.1 Biot-Savart's law (Laplace's law)

2. The magnetic induction at a point P which is at adistance of 4 cm from a long current carryingwire is 10–8 T. The induction at a distance 12 cmfrom same current carrying wire isa) 1.11 × 10–7 T b) 3.33 × 10–9 Tc) 3 × 10–3 T d) 3.3 × 10–7 T

3. A vertical straight conductor carries a currentvertically upwards. A point P lies to the east of itat a small distance and another point Q lies to thewest at the same distance. The magnetic field atP isa) greater than at Qb) same as at Qc) less than at Qd) greater or less than of Q depending upon the

strength of the current4. If a copper rod carries a direct current, the

magnetic field associated with the current will bea) only inside the rodb) only outside the rodc) both inside and outside the rodd) neither inside nor outside the rod

5. If a long hollow copper pie carries a direct current,the magnetic field associated with the current willbe

a) only inside the pipeb) only outside the pipec) neither inside nor outside the piped) both inside and outside the pipe



6. A helium nucleus makes a full rotation in a radius0.8 metre in two seconds. The value of themagnetic field B at the centre of the circle willbe

a)0

1910

b) 10–19 0

c) 2 × 10–10 0

d)0

10102

7. Two identical coils carrying equal current have acommon centre but their planes are at right anglesto each other. What is the ratio of the magnitudesof the resultant magnetic field and the field dueto one coil alone at the centre ?

a) 2 b) 2

c) 3 d) 18. Two circular coils are made of two identical wires

of same length. If the number of turns of coil are4 and 2 then the ratio of magnetic induction atcentre will bea) 4 : 1 b) 1 : 4c) 1 : 2 d) 2 : 1



9. The magnetic induction at a point on the axis of acircular current carrying coil at a distance equalto the radius of coil carrying a current of 0.5 A is

a) T102a 7 b) T102

a 7

c) T10a2

7

d) T10a

2 7

10. The ratio of magnetic induction at a point alongthe axis of a circular coil of radius 'a' at a distance'x' to a point where x tends to zero is [x >> a]a) x3/a3 b) a3/x3

c) 2a3/x2 d) 2x3/a2

11. A wire of length L carrying a current I is bentinto a circle. The magnitude of the magnetic fieldat the centre of the circle is

a)L

I0b)

L2

I0

c)L

I2 0d)

L2

I0



7MEEC

12. The electric current in a circular coil of two turnsproduces a magnetic induction of 0.2 T at itscentre. The coil is unwound and rewound into acircular coil of four turns. The magnetic inductionat the centre of the coil now is, in tesla, (if samecurrent flows in the coil)a) 0.2 b) 0.4c) 0.6 d) 0.8

13. A circular coil of radius r carries a current I. Themagnetic field at its centre is B. At what distancefrom the centre, on the axis of the coil the magneticfield will be B/8 ?a) 3r b) 2r

c) r3 d) r2

12.5Force acting on a current carrying conductor

in a magnetic field

14. Assertion : An electron and proton enters amagnetic field with equal velocities, then, the forceexperienced by the proton will be more thanelectron.Reason : The mass of proton is 1837 times morethan electron.a) Assertion is True, Reason is True; Reason is

a correct explanation for Assertion.b) Assertion is True, Reason is True; Reason is

not a correct explanation for Assertionc) Assertion is True, Reason is Falsed) Assertion is False, Reason is True

15. A very high magnetic field is applied to a stationarycharge. Then the charge experiencesa) no forceb) a force in the direction of magnetic fieldc) a force perpendicular to the magnetic fieldd) a force in an arbitrary direction

16. An electron having a charge 'e' moves with avelocity 'v' in the X-direction. A magnetic fieldacts on it in the Y-direction. The force on theelectron acts ina) X-direction b) Y-directionc) Z-direction d) negative Z-direction

17. A particle with 10–11 coulomb of charge and10–7 kg mass is moving with a velocity of 108 m/salong the y-axis. A uniform static magnetic fieldB = 0.5 tesla is acting along the x-direction. Theforce on the particle is

a) 5 × 10–11 N along

i

b) 5 × 10–4 N along

k

c) 5 × 10–11 N along

j

d) 5 × 10–3 N along

k

18. A current carrying straight wire is kept along theaxis of a circular loop carrying a current. Thestraight wirea) will exert an inward force on the circular loopb) will exert on outward force on the circular loopc) will exert a force on the circular loop parallel

to itselfd) will not exert any force on the circular

19. A particle of charge –16 × 10–18 C moving withvelocity 10 m/s along the X-axis enters a regionwhere a magnetic field of induction B is alongY-axis and electric field of magneitude 104 V/mis along the negative Z-axis. If the chargedparticle continues moving along the X-axis, themagnitude of B is

Y

Xv

O

B

E

Z

a) 103 Wb/m2 b) 105 Wb/m2

c) 106 Wb/m2 d) 107 Wb/m2


20. A current carrying wire is placed along east-westin a magnetic field directed northwards. If thecurrent in the wire is directed eastwards, whatwill be the direction of force on the wire ?a) due west b) due southc) vertically upwards d) vertically downwards

12.7 Force between two infinitely long current


21. Two long parallel axis, separated by a distance Rhave equal current I flowing in each of them.The magnetic field of one exerts a force F on theother. The distance R is increased to 2R and thecurrent in each wire is reduced from I to I/2.What is he force between them now ?a) 4 F b) Fc) F/4 d) F/8


22. While defining value of one ampere of steadycurrent, which of the following condition needsto be taken into consideration ?a) Dimensions of two conductorsb) Distance between two conductorsc) Amount of force produced between themd) All of the above



8MEEC

23. A horizontal conducting wire of length 0.1 mcarries a current of 4 A. If mass of the wire is7.5 × 10–5 kg and g = 10 m/s2, the uniformmagnetic induction required to support the weightof the wire isa) 1.675 × 10–3 T b) 1.775 × 10–3 Tc) 1.875 × 10–3 T d) 1.975 × 10–3 T


24. A rectangular loop is acted upon by two forcesof same magnitude but opposite directions. Thenet force acting on the loop isa) maximumb) zeroc) equal to magnitude of torqued) one

25. Which of the following is experienced by acurrent carrying loop in a uniform magnetic field?a) Force onlyb) Torque onlyc) Both torque and forced) Neither torque nor force

26. A current carrying loop is placed in a uniformmagnetic field. The torque acting on it does notdepend upon thea) shape of loopb) area of loopc) number of turnsd) angle between normal of coil and magnetic

field27. The ( – ) graph for a coil is

a)

00

9001800

b)

00

9001800

c)

00

9001800

d)

00

9001800

28. A current loop of area A, number of turns N isplaced in a uniform magnetic induction B. The

angle between the plane of the loop and

B is .

The torque acting on the loop will bea) NIAB b) NIAB sin c) NIAB cos d) NIAB tan

29. Two wires of same length are shaped into asquare and a circle. If they carry same current,

ratio of the magnetic moment isa) 2 : b) : 2c) : 4 d) 4 :

Miscellaneous

30. A 2 MeV proton is moving perpendicular to auniform magnetic field of 2.5 T. The force onproton isa) 8 × 10–10 N b) 4 × 10–10 Nc) 1.2 × 10–10 N d) 7.84 × 10–12 N

31. A length of wire carries a steady current. It isbent first to form a circular plane loop of oneturn. The magnetic field at centre of loop is B.The same length is now bent to give a doubleloop of smaller radius. The magnetic field at thecentre caused by same current isa) B b) 2 Bc) 3 B d) 4 B

32. Which of the following graph shows the variationof magnetic field B, with distance for a longcurrent carrying conductor ?

a)

B

r

b)

B

r

c)

B

r

d)

B

r

33. A homogeneous electric field

E and a uniform

magnetic field

B are pointing in the same

direction. A proton is projected with its velocity

parallel to E . It will

a) go on moving in the same direction withincreasing velocity

b) go on moving in the same direction withconstant velocity

c) turn to its rightd) turn to its left

34. A wire carrying current I and other carrying 2I inthe same direction produce magnetic field at themid-point. What will be the field, when 2I wire isswitched off ?

a)2

Bb) 2B

c) B d) 4B



9MEEC

35. Two electrons move parallel to each other withequal speed v. The ratio of magnetic and electricalforces between them is

a)c

vb)

v

c

c) 2

2

c

vd) 2

2

v

c

36. A uniform conducting wire ABC has a mass of10 g. A current of 2 A flows through it. The wireis kept in a uniform magnetic field B = 2 T. Theacceleration of the wire will be

×

×

×

×

×

×

×

×

×

×

×

×

×

×

×

×

4 cm

5 cm

A

B

C

Y

Z

X

a) zerob) 12 m/s2 along Y-axisc) 1.2 × 10–3 m/s2 along Y-axisd) 0.6 × 10–3 m/s2 along Y-axis

37. The work done by a magnetic field on movingcharge is

a) zero because

F acts parallel to

v

b) positive because F acts perpendicular to

v

c) zero because

F acts perpendicular to

v

d) negative because

F acts parallel to

v38. For a given perimeter in plane, following are some

shapes mentioned. Choose the shape for the loopsuch that which when placed inside magnetic fieldwill have maximum torque acting on ita) Square b) Rectanglec) Circle d) Sphere

39. Three long straight wires are connected parallelto each other across a battery of negligible internalresistance. The ratio of their resistance are3 : 4 : 5. What is the ratio of distances of middlewire from the others if the net force experiencedby it is zero ?a) 4 : 3 b) 3 : 1c) 5 : 3 d) 2 : 3

40. A horizontal rod of mass 10 g and length 10 cm isplaced on a smooth plane inclined at an angle of600 with the horizontal, with the length of the rodparallel to the edge of the inclined plane. A uniformmagnetic field of induction B is applied verticallydownwards. If the current through the rod is 1.73

ampere, then the value of B for which the rodremains stationary on the inclined plane isa) 1.73 T b) (1.73)–1 T

c) 1 T d) T)73.1(2

41. A particle of charge q and mass m is moving alongthe X-axis with a velocity v and enters a regionof electric field E and magnetic field B as shownin figure below. For which figure the net force onthe charge may be zero ?

a)

Y

B

X

EZ

vq

b)

Y

B

X

E

Z

vq

c)

Y

B

X

E

Z

vq

B

d)

Y

E

X

Z

vq

B

42. In Bohr's model of hydrogen atom, the electroncirculates around nucleus in a path of radius 0.5 Åat a frequency of 6.8 × 1015 rev/s. The magneticfield at the centre will bea) 13.7 T b) 1 Tc) 13.7 gauss d) 13 gauss

43. A horizontal wire carries 200 A current belowwhich another wire of linear density 20 × 10–3 kg/mcarrying a current is kept at 2 cm distance. If thewire kept below hangs in air, what is the currentin this wire ?a) 100 A b) 9.8 Ac) 98 A d) 48 A

Competitive Thinking

12.1 Biot-Savart's law (Laplace's Law)

1. The magnetic field near a current carryingconductor is given bya) Coulomb's law b) Lenz' law



10MEEC

c) Biot-Savart's law d) Kirchoff's law2. Two very thin metallic wires placed along X and

Y-axis carry equal currents as shown here. ABand CD are lines at 450 with the axes with originof axes at O. The magnetic field will be zero onthe line

YB

X

DA

C

OI

I

a) ABb) CDc) segment OB only of line ABd) segment OC only of line CD

3. Two identical long conducting wires AOB andCOD are placed ar right angle to each other,which one above other such that O is the commonpoint for the two. The wires carry I

1 and I

2

currents, respectively. Point P is lying at distanced from O along a direction perpendicular to theplane containing the wires. The magnetic field atthe point P will be

a)

2

10

I

I

d2 b) 210 IId2

c) 22

21

0 IId2

d) 2/12

221

0 IId2

4. A long straight wire carrying current of 30 A isplaced in an external uniform magnetic field ofinduction 4 × 10–4 T. The magnetic field is actingparallel to the direction of current. The magnitudeof the resultant magnetic induction in tesla at apoint 2.0 cm away from the wire isa) 10–4 b) 3 × 10–4

c) 5 × 10–4 d) 6 × 10–4



5. A current carrying circular loop is freely suspendedby a long thread. The plane of the loop will pointin the directiona) wherever left freeb) north-southc) east-westd) at 450 with the east-west direction

6. A current of 0.1 A circulates around a coil of 100turns and has a radius equal to 5 cm. The magneticfield set up at the centre of the coil is(

0 = 4 × 10–7 weber/ampere metre)

a) 4 × 10–5 tesla b) 8 × 10–5 tesla

c) 4 × 10–5 tesla d) 2 × 10–5 tesla7. A long wire carrying current I is bent into a circle

of one turn and magnetic field at the centre ofcoil is B. It is then bent into a circular loop of nturns of equal radii, what will be the magneticfield at the centre of new coil ?

a) nB b) n2 B

c)B

n 2

d) 2n

B

8. A long, straight wire is turned into a loop of radius10 cm (see figure). If a current of 8 ampere ispassed through the loop, then the value of themagnetic field and its direction at the centre C ofthe loop shall be close to

8 ampere

10 cm

C

a) 5.0 × 10–5 newton/(amp-metre), upward

b) 3.4 × 10–5 newton/(amp-metre), upward

c) 1.6 × 10–5 newton/(amp-metre), downward

d) 1.6 × 10–5 newton/(amp-metre), upward



9. Magnetic field due to a ring having n turns at adistance x on its axis is proportional to (if a =radius of ring)

a) )xa(

a22 b) 2/322

2

)xa(

a

c) 2/322

2

)xa(

na

d) 2/322

22

)xa(

an

10. A long straight wire of a circular cross section(radius a) carries a steady current I and thecurrent I is uniformly distributed across this cross-section. Which of the following plots representsthe variation of magnitude of magnetic field Bwith distance r from the centre of the wire ?

a)

B

ra

b)

B

ra



11MEEC

c)

B

ra

d)

B

ra

11. The magnetic field due to a current carryingcircular loop of radius 3 cm at a point on the axisat a distance 4 cm from the centre is 54 T. Whatwill be its value at the centre of the loop ?a) 250 T b) 150 Tc) 125 T d) 75 T

12. Magnetic fields at two points on the axis of acircular coil at a distance of 0.05 m and 0.2 mfrom the centre are in the ratio 8 : 1. The radiusof the coil isa) 1.0 m b) 0.1 mc) 0.15 m d) 0.2 m

12.5 Force acting on a current carrying conductor

in a magnetic field

13. If a proton is projected in a direction perpendicularto a uniform magnetic field with velocity v andan electron is projected along the lines of force,what will happen to the proton and electron ?a) the electron will travel along a circle with

constant speed and the proton will move alonga straight line

b) proton will move in a circle with constant speedand there will be no effect on the motion ofelectron

c) there will not be any effect on the motion ofelectron and proton

d) the electron and proton both will follow thepath of a parabola

14. A charged particle moving with velocity v issubjected to electric field E and magnetic fieldB. The particle will go undeflected ifa) E is perpendicular to Bb) E is parallel to v and perpendicular to Bc) E and B both are parallel to vd) E, B and v are mutually perpendicular but

B

Ev

15. A charged particle is moving along a magneticfield line. The magnetic force on the particle isa) along its velocityb) opposite to its velocityc) perpendicular to its velocityd) zero

16. If a particle of charge 10–12 coulomb moving along

the x -direction with a velocity 105 m/s experiences

a force of 10–10 newton in

y -direction due to

magnetic field, then the minimum magnetic fieldis

a) 6.25 × 103 tesla in

z -direction

b) 10–15 tesla in

z -direction

c) 6.25 × 10–3 tesla in

z -direction

d) 10–3 tesla in

z -direction17. A current of 5 ampere is flowing in a wire of

length 1.5 metre. A force of 7.5 N acts on it whenit is placed in a uniform magnetic field of 2 T.The angle between the magnetic field and thedirection of the current isa) 300 b) 450

c) 600 d) 900

18. A conductor in the form of a right angle ABCwith AB = 3 cm and BC = 4 cm carries a currentof 10 A. There is a uniform magnetic field of 5 Tperpendicular to the plane of the conductor. Theforce on the conductor will bea) 1.5 N b) 2.0 Nc) 2.5 N d) 3.5 N

19. 1 Tesla =a) 1 Wb/m b) 1 J/A mc) 1 N/A m d) 1 A m/N


20. The electron in the beam of a television tube movehorizontally from south to north. The verticalcomponent of the earth's magnetic field pointsdown. The electron is deflected towardsa) westb) no deflectionc) eastd) north to south

21. A vertical wire carrying a current in the upwarddirection is placed in horizontal magnetic fielddirected towards north. The wire will experiencea force directed towardsa) north b) southc) east d) west

22. An electron moving with a uniform velocity alongthe positive x-direction enters a magnetic fielddirected along the positive y-direction. The forceon the electron is directed alonga) positive y-directionb) negative y-directionc) positive z-directiond) negative z-direction

12.7 Force between two infinitely long current


23. Two free parallel wires carrying currents inopposite directiona) attract each other



12MEEC

b) repel each otherc) neither attract nor repeld) get rotated to be perpendicular to each other

24. Two parallel beams of electrons moving in thesame direction produce a mutual forcea) of attraction in plane of paperb) of repulstion in plane of paperc) upwards perpendicular to plane of paperd) downwards perpendicular to plane of paper

25. Two long conductors separated by a distance dcarry currents I

1 and I

2 in the same direction exert

a force F on each other. Now the current in oneof them is increased two times and its direction isreversed. The distance is also increased to 3a.The net value of the force between them is

a) –2F b)3

F

c)3

F2 d)

3

F

26. Two thin long parallel wires separated by adistance b are carrying a current I A each. Themagnitude of the force per unit length exerted byone wire on the other is

a) 2

20

b

Ib)

b2

I20

c)b2

I0

d) 20

b2

I

27. Two thin, long, parallel wires, separated by adistance 'd' carry a current of 'I' A in the samedirection. They will

a) attract each other with a force of 2

20

d2

I

b) repel each other with a force of 2

20

d2

I

c) attract each other with a force of d2

I20

d) repeal each other with a force of d2

I20

28. Two long parallel wires carrying equal currentseparated by 1 m, exert a force of 2 × 10–7 N/mm on one another. The current flowing throughthem isa) 2.0 A b) 2.0 × 10–1 Ac) 1.0 A d) 1.0 × 10–7 A

29. A, B and C are parallel conductors of equal lengthcarrying currents I, I and 2I respectively. Distancebetween A and B is x. Distance between B andC is also x. F

1 is the force exerted by B on A and

F2 is the force exerted by B on A. Choose the

correct answer

x x

A B C

I I 2I

a) F1 = 2F

2b) F

2 = 2F

1

c) F1 = F

2d) F

1 = –F

2

30. Three long, straight and parallel wires carryingcurrents are arranged as shown in figure. Theforce experienced by 10 cm length of wire Q is

P Q R

20 A 10 A 30 A

2 cm 10 cm

a) 1.4 × 10–4 N towards the rightb) 1.4 × 10–4 N towards the leftc) 2.6 × 10–4 N to the rightd) 2.6 × 10–4 N to the left


31. A rectangular loop carrying a current I is placedin a uniform magnetic field B. The area enclosedby the loop is A. If there are n turns in the loop,the torque acting on the loop is given by

a)

BAnI b)

BAnI

c) )BAI(n

1

d) )BAI(n

1

32. A triangular loop of side l carries a current I. It isplaced in a magnetic field B such that the planeof the loop is in the direction of B. The torque onthe loop isa) zero b) IBl

c) 22BI2

3l d) 2IB

4

3l

33. A current I flows in a circular coil of radius r. Ifthe coil is placed in a uniform magnetic field Bwith its plane parallel to the field, magnitude ofthe torque that acts on the coil isa) zero b) 2rIBc) r2IB d) 22IB

34. The magnetic moment of a current (i) carryingcircular coil of radius (r) and number of turns (n)varies are



13MEEC

a) 1/r2 b) 1/rc) r d) r2

35. A current loop in a magnetic fielda) experiences a torque whether the field is

uniform or non uniform in all orientationb) can be in equilibrium in one orientationc) can be in equilibrium in two orientation both

the equilibrium states are unstabled) can be in equilibrium in two orientations, one

stable while the other is unstable

36. Magnetic dipole moment

M of the coil, placed

in uniform magnetic field of induction

B does

not depend ona) number of turns of coilb) current through coilc) area of the cross-sectiond) magnetic field of induction

Miscellaneous

37. A coil of 100 turns and area 2 × 10–2 m2, pivotedabout a vertical diameter in a uniform magneticfield carries a current of 5 A. When the coil isheld with its plane in North–South direction, itexperiences a torque of 0.3 N m. When the planeis in East–West direction the torque is 0.4 N m.The value of magnetic induction is (Neglectearth's magnetic field)a) 0.2 T b) 0.3 Tc) 0.4 T d) 0.05 T

38. When a proton is released from rest in a room, itstarts with an initial acceleration a

0 towards west.

When it is projected towards north with a speedv

0 it moves with an initial acceleration 3a

0 toward

west. The electric and magnetic fields in the roomare

a) upev

2ma west,

e

ma

0

00

b) owndev

2ma west,

e

ma

0

00

c) upev

3ma east,

e

ma

0

00

d) owndev

3ma east,

e

ma

0

00

39. The uniform electric field and a uniform magneticfield are produced, pointed in the same direction.An electron is projected with its velocity pointingin the same direction. Thena) the electron will turn to its right

b) the electron will turn to its leftc) the electron velocity will increase in magnituded) the electron velocity will decrease in magnitude

40. A conductor lies along the z-axis at –1.5 < z < 1.5m

and carries a fixed current of 10.0 A in za

direction (see figure). For a field

B = 3.0 × 10–4

e–0.2x Ta y

, find the power required to move the

conductor at constant speed to x = 2.0 m, y = 0 min 5 × 10–3 s. Assume parallel motion along thex-axis

1.5

Z

I

B y

– 1.5x

2.0

a) 1.57 W b) 2.97 Wc) 14.85 W d) 29.7 W

41. Two current carrying coils have radii r and 2rand have same magnetic induction at their centres.The ratio of voltage applied across them isa) 1 : 2 b) 2 : 1c) 1 : 4 d) 1 : 8

42. Mangetic induction produced at the centre of acircular loop carrying current is 'B'. The magneticmoment of the loop of radius 'R' is(

0 = permeability of free space)

a)0

3

2

BR

b)0

3BR2

c)0

2

2

BR

d)0

2BR2

43. The electron in the hydrogen atom circles roundthe proton with a speed of 2.2 × 106 ms–1 in anorbit of radius 5 × 10–11 m. What magnetic fielddoes it produce at the proton ?a) 14.08 T b) 13.08 Tc) 10.08 T d) 12.08 T

44. If two streams of protons move paralle to eachother in the same direction, then theya) do not exert any force on each otherb) repel each other



14MEEC

c) attract each otherd) get rotated to be perpendicular to each other

Cathode ray oscilloscope

A moving charged particle experiencea force in electric and magnetic fields.This concept is used in making a

(CRO) or(CRT).

Same concept is used in designing highenergy accelerators like cyclotron,betatron.Cathode-ray oscilloscopes, electronic-display devices contain a cathode-raytube (CRT) that generates an electronbeam. The beam is used to produce visiblepatterns or graphs, on a phosphorescentscreen.In all modern CRT monitors and televisionsthe beams are bent by magnetic deflection,a varying magnetic filed generated by coilsand driven by electronic circuits.

cathode ray oscillographcathode ray tube




15


16


17


18


19


20


21


22


23


24


25

MEEC 12 Magnetic Effect of Electric Current · 2020. 4. 6. · MEEC 1 12 Magnetic Effect of...

Documents

Transcript of MEEC 12 Magnetic Effect of Electric Current · 2020. 4. 6. · MEEC 1 12 Magnetic Effect of...