ALPS_ Physics - 2203 Magnetism, Electromagnetic Induction

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VMC | Physics 1 ALPS-2203

ALPS_ Physics - 2203

Syllabus Magnetism, Electromagnetic Induction

* Mark questions are more than one option correct type.

---------------------------------------------------------------------- DAY-1 -----------------------------------------------------------------------

1. An infinitely long conductor is bent at a point O at an angle as shown. The magnetic field at a point P

distance r along the angle bisector is : [ ]

(A) 0( / 4 ) (2 / )[1 cos( / 2)] / sin( / 2)i r

(B) 0( / 4 ) ( / )cot( / 2)i r

(C) 0( / 2 ) ( / )cot( / 2)i r

(D) 0( / 4 ) ( / )sin( / 2)i r

2. A magnetic field directed along Z-axis varies as 0 / ,B B x a where a is a positive constant. A square loop

of side l and made of copper is placed with its edges parallel to X and Y axes. If the loop is made to move

with a constant velocity 0v directed along X-axis, the emf induced is : [ ]

(A) 20 0( ) /B v l a (B) 0 0( )B v l

(C) 20 0( ) / 2B v l a (D) 3 2

0 0( ) /B v l a

3. A parallel plate capacitor consists of square plates of edge length a separated by a distance d that is much

smaller that the edge length. It is charged to a potential V and made to move with a constant velocity v

directed along one of its edges. How much magnetic field exists inside the capacitor?

(A) 0 0vV

d

(B) 0 0vV

a

(C) 0 0

2

dvV

a

(D) None of these

4. A wire of uniform cross-section is drawn from a piece of mass m of a metal of density d and resistivity .

The ends of the wire are joined to make a planar closed loop and the loop is placed in a uniform magnetic

field that varies with time t according to equation B t , where is a positive constant. What maximum

current can you obtain in the loop by properly selecting shape and dimensions of the loop?

(A) /( )m d (B) /(2 )m d [ ]

(C) /(4 )m d (D) /(8 )m d

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5. A metallic coin is sliding on a long frictionless horizontal table. A

uniform vertical magnetic field B exists between points 1P and 2P of this

table as shown. Which figure below accurately depicts the speed of the

coin as it slides across the table from one end to another ? [ ]

(A) (B) (C) (D)

6. A particle of mass m and charge q is moving with a constant speed in a region of space, where a uniform

and constant magnetic field B and an electric filed E coexist in mutually perpendicular horizontal

directions in addition to gravitational field of intensity g. After the magnetic and electric fields are switched

off, the minimum kinetic energy of the particle is observed to be half of the kinetic energy when all these

fields were coexisting. What can you certainly conclude for component of velocity of the particle along the

direction of the magnetic field?

(A) It is zero

(B) It is

2 2E mg

B qB

pointing opposite to B

(C) It is

2 2E mg

B qB

pointing in the direction of B

(D) It is

2 2E mg

B qB

pointing either in direction of or opposite to B

7. Two coaxial circular coils of radii a and b are separated by a large distance x and carry equal currents I. If a

>> b, what is the force of mutual interaction between them. [ ]

(A) 2 2

0

2 2 1.5( )

I a b

a x

(B)

20

2 2 1.5

3

( )

I abx

a x

(C) 2 3

0

2 2 2( )

I a b

a x

(D)

2 2 202 2 2.5

3

2( )

I a b x

a x

8. Consider a quarter circular conducting ring of large radius r with its centre at

the origin, where a magnetic dipole of moment m is placed as shown in the

figure. If the ring rotates at a constant angular velocity about the y-axis,

electromotive force induced between its ends is: [ ]

(A) Zero (B) 0 /(2 )m r

(C) 0 /(4 )m r (D) 0 /(8 )m r

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9. The magnetic field at the centre O of the arc formed by bending an infinite wire as shown in the figure is:

(A) 710

2 ( 2 )ir

(B) 710

2 ( 2 )4

ir

[ ]

(C) 710

( 2 )ir

(D) 710

2 2 14

ir

10. Current I flowing along edges of one face of a cube as shown in the figure-I, produces magnetic field

0ˆB B j at the centre of the cube. Consider another identical cube, where the current I flows along the path

shown in the figure-II. How much magnetic field exists at the centre of the second cube? [ ]

(A) Zero (B) 0( )B i j k (C) 0ˆˆ ˆ( )B i j k (D) 0

ˆˆ ˆ( )B i j k

---------------------------------------------------------------------- DAY-2 -----------------------------------------------------------------------

*11. Several -particles of different speeds enter a uniform magnetic field

confined into a cylindrical region. If all the -particle enter the field radially,

what can you say about time intervals spent by them 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

*12. A long thin wooden cylindrical pipe of radius R carrying a

uniform surface charge density , is rotating about its axis

with an angular veocity that increases slowly with time t as

kt , where k is a positive constant. Which of the following

statements is /are correct for the rigion inside the pipe?

(A) Both the magnetic and the electric fields are uniform and constant

(B) The magnetic field is uniform but not constant and the electric field is constant but not uniform

(C) The magnetic field is constant but not uniform and the electric field is uniform but not constant

(D) Total energy denstiy u due to both the fields varies with time as 2u a bt , where a and b are

positive constants.

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*13. In a moving coil galvanometer, the number of turns 24,N area of the coil 3 22 10 , A m and the

magnetic field strength 0.2 .B T To increase its current sensitivity by 25% we may : [ ]

(A) Increase B to 0.30 T (B) Increase A to 3 22.5 10 m

(C) Increase N to 30 (D) None of the above

*14. In a region of free space, where a uniform and constant electric field of intensity E and a magnetic field of

induction B coexists, an electron projected with speed v in the positive x-direction, moves undeviated

without change in speed. In addition, an electron projected with velocity v in the positive y-direction in this

region ; also, moves undeviated without change in speed. Which of the following conclusions can you

make?

(A) | | | |E v B (B) | | | |E v B [ ]

(C) The electric field is perpendicular to the x-y plane

(D) The magnetic field is either at 45° to 135° with the positive x-direction

*15. A circular conducting loop of radius 0r and having resistance per unit length is

placed in a constant magnetic field B which is perpendicular to plane of loop.

The ends P and Q of the wire are pulled in opposite directions with a constant

velocity v such that loop remains circular and the radius of the loop goes on

decreasing, then choose the correct options. [ ]

(A) Magnitude of the emf induced in the loop as a function of time t is 022

r vtBv

(B) Magnitude of the emf induced in the loop as a function of time t is 02vt

Bv r

(C) Current induced in the loop is2

Bv

(D) Current induced in the loop is

Bv

*16. A positively charged particle P crosses a region of uniform electric field of intensity E. Velocity u of the

particle at the entry on the left side of the region is perpendicular to the electric field as shown in the first

figure. Speed of the particle at exit on the right side is 1v . Now the experiment is repeated with a uniform

magnetic field of induction B superimposed on the electric field as shown in the second figure, keeping

entry velocity of the particle unchanged. In this experiment, speed of the particle at exit on the right side is

2v . What can you conclude regarding the speeds v1 and v2? [ ]

(A) If 2 1, thenE

u v vB

(B) 2 1If , thenE

u v vB

(C) 2 1If , thenE

u v vB

(D) 2 1If , thenE

u v vB

× × × × × × ×

× × × × × × ×

× × × × × × ×

× × × × × × ×

B

P A Q v v

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*17. In a region, magnetic field along x-axis changes according to the graph given in figure below. A positively

charged particle is projected at an angle 0 with the positive x-axis toward positive y-axis in x-y plane. If

time period, pitch and radius of helix path are 0 0,T P and 0 ,R respectively, then select the correct

statements. [ ]

(A) At 0

2

Tt , coordinates of charge are 0

0, 0, 22

PR

(B) At 03

2

Tt , coordinates of charge are 0

0

3, 0, 2

2

PR

(C) At 0

2

Tt , coordinates of charge are 0 0( ,0, 2 )P R

(D) At 03

2

Tt . Coordinates of charge are 0 0(3 , 0, 2 )P R

*18. In cyclotron (particle accelerator), an ion is made to travel successively along semicircles of increasing

radii under the action of a magnetic field. The angular velocity of the ion is independent of :

(A) Speed of the ion (B) Radius of the circle [ ]

(C) Mass of the ion (D) Charge of the ion

*19. An aircraft is flying at a level height in presence of the magnetic field of the Earth. If an electic bulb is

connected between the two extreme ends of the wings: [ ]

(A) A voltage will induce across the wings

(B) No voltage will induce across the wings

(C) The bulb will glow

(D) The bulb will not glow

*20. Four uniform wires FG, GH HI and IF, each of length l and having

resistance R, 2R, 3R and 4R are connected together to form a square

FGHI as shown in figure. The square is placed in a uniform magnetic

field whose induction varies with time according to the law 0B B t .

Choose the correct options. [ ]

(A) Current induced in the loop is 2

0

10

B

R

(B) Potential difference across ends of wire FG is 2

0

4

B

(C) Potential difference across ends is different for the four wires

(D) Potential difference across ends of wire FG is 2

03

20

B

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---------------------------------------------------------------------- DAY-3 -----------------------------------------------------------------------

PARAGRAPH FOR QUESTIONS 21 – 23 [ ]

A charged particle of charge 1C and mass 10gm is moving with velocity 10 i m/s in horizontal plane consisting of

magnetic field –0.1 k T of width 3

2m and electric field –0.1 j N/C of width d. Particle enters the magnetic field at

t = 0 perpendicularly and follows the path as shown in the figure and strikes the wall AB perpendicularly at A

(neglect gravity)

21. The time t after which it strikes the wall is:

(A) 1.2 s (B) 0.97 s (C) 1.07 s (D) 1.98 s

22. The width d of electric field is:

(A) 5 3 m (B) 5

32

m (C) 10 3 m (D) 5

34

m

23. Taking O as origin, y-coordinate of A will be :

(A) 3.75 m (B) 0.50 m (C) 4.25 m (D) 3.25 m

ARAGRAPH FOR QUESTIONS 24 – 25 [ ]

A charged particle of mass m and charge q is projected on a rough horizontal XY plane. Both electric and magnetic

fields given by ˆ10 / E k N C and magnetic field ˆ5 B k Tesla are present in the region. The particle enters into

the magnetic field at (4, 0, 0) m with a velocity ˆ50 j m/sec. The particle starts into a curved path on the plane. If

coefficient of friction between particle and plane is 1

3 , then: (take qE = 2mg, g = 10 m/s

2).

24. Radius of curvature of the path followed by particle, initially is:

(A) 5 m (B) 2.5 m (C) 1.25 m (D) 10 m

25. The time after which particle comes to rest is :

(A) 5s (B) 4s (C) 3s (D) 1s

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PARAGRAPH FOR QUESTIONS 26 – 28

A horizontal rectangular plastic pipe of width w and height h, is filled with mercury of resistivity . An

overpressure P is produced by a turbine which drives this fluid with a constant speed 0v . The two opposite vertical

walls of a section of the pipe with length L are made of copper.

The motion of a real fluid is very complicated. To simplify the situation we assume the following :

Although the fluid is viscous, its speed is uniform over the entire cross-section.

The speed of the fluid is always proportional to the net external force acting upon it.

The fluid is incompressible.

The copper walls are electrically shorted externally and a uniform magnetic field B is applied vertically upward

only in this section. The set-up is illustrated in the figure, with the unit vectors ˆ ˆ ˆ, ,x y z to be used in the solution.

26. Find the force acting on the fluid due to magnetic field (in terms of L, B, h, w, and the new velocity v).

(A) 2vB Lhw

(B) 2B wvLh (C)

vBLhw

(D)

2B Lv

P

27. Derive an expression for the new speed v of the fluid (in terms of 0v , P, L, B and ) after the magnetic

field is applied.

(A) 02

01

v P

v B L

(B) 0

20

v P

P v B L

(C) 0

20

v P

P v B L

(D) 0 2

0

1P

vv B L

28. Derive an expression for the additional power that must be supplied by the turbine to increase the speed to

its original value 0v .

(A) 2 20v B whL

(B)

20v BwhL

(C)

2 202v B whL

(D) 0hwPv

PARAGRAPH FOR QUESTIONS 29 – 30 [ ]

A magnetic field 0 ˆ

B yB k

a is into the paper in the +z direction. B0

and a are positive constants. A square loop EFGH of side a, mass m

and resistance R, in x-y plane, starts falling under the influence of

gravity. Assume x-axis is horizontal and y is vertically downward.

O x

y

E F

G H 4

1

2

3

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29. The magnitude and direction of the induced current in the loop when its speed is v is :

(A) 0B av

R, anticlockwise (B) 0B av

R, clockwise

(C) 0B v

aR, anticlockwise (D) None of these

30. The expression for the speed of the loop v(t) is :

(A)

2 20

2 20

1

B a t

mRmg

eB a

(B)

2 20

2 20

1

B a t

mRRmg

eB a

(C)

2 20

2 20

B a t

mRRmg

eB a

(D) None of these

---------------------------------------------------------------------- DAY-4 -----------------------------------------------------------------------

31. Match column I with column II [ ]

Column I Column II

(A) A charge particle is moving in gravity free space

having uniform electric and magnetic fields (p) Velocity of the particle may be constant

(B) A charge particle is moving in a region having uniform electric, magnetic and gravitational fields

(q) Path of the particle may be straight line

(C) A charge particle is moving in a region having

uniform magnetic and gravitational fields (r) Path of the particle may be circular

(D) A charge particle is moving in a region having only uniform electric field

(s) Path of the particle may be helical

32. Column I gives some incomplete statements. Column II contains the missing portions of statements

contained in column I. Match appropriately. [ ]

Column I Column II

(A) A rod rotates in a uniform transverse

magnetic field as shown, about hinge at

O. Potential difference between point A

and B

(p) may be zero

(B) A conducting loop is moved in a region

of transverse magnetic field, as shown.

Value of induced current i at this instant

(q) must be zero

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(C) A conducting loop is placed in a

transverse magnetic field as shown. The

magnetic field changes with time as

(10 2 )B t Tesla. Value of induced

current i at an instant t

(r) is/may be negative

(D) A square loop is rotated with constant

about diagonal in a region of uniform

magnetic field as shown. Value of

induced current i at an instant

(s) is/may be positive

33. Two long parallel wires carrying equal currents in opposite directions are placed at x a parallel to Y-

axis with z = 0. Then : [ ]

Column I Column II

(A) Magnetic field B1 at origin O (p) 0

3

i

a

(B) Magnetic field B2 at (2a, 0, 0) (q) 0

2

i

a

(C) Magnetic field at (0, a, 0) (r) 0

i

a

(D) If wire carries current in the same direction, then magnetic field at origin (s) Zero

34. The central cross-section of a long cylindrical region containing uniform but time varying magnetic field B

is shown. A particle of constant mass and variable positive charge moves in a circle in the plane, so that the

radius of the circle remains constant. [ ]

V V

q, m

Column I Column II

(A) If the magnetic field is increased by 2%, the speed of the particle will (p) decrease

(B) If the magnetic field is decreased by 4%, the speed of the particle will (q) increase

(C) If the magnetic field is increased by 2%, the charge of the particle will (r) change by 1%

(D) If the magnetic field is decreased by 4%, the charge of the particle

will (s) change by 2%

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35. Magnetic field B0 is present in the region X = 0 to X = L along –ve z-axis. A

charge particle having charge q and mass m enters in the magnetic field along x-

axis with speed 0v . If 0

02

mvL

qB, angle of deviation is 1 and time spent in

magnetic field is 1t and if 0

0

3

2

mvL

qB angle of deviation is 2 and time spent in

magnetic field is 2t , then [ ]

Column I Column II

(A) 1 is (p) 6

m

qB

(B) 2 is (q) 3

m

qB

(C) 1t is (r) / 3

(D) 2t is (s) / 6

(t) / 2

36. A conductor is bent in the form of concentric semicircles as shown in the figure. Radius of semicircles is

increasing by a factor of 2. The magnetic field at the point O is 0 , i

na where n is______. [ ]

37. A uniformly conducting wire is bent to form a ring of mass 'm' and radius ‘r’ and the ring is placed

on a rough horizontal surface with its plane horizontal. There exists a uniform and constant

horizontal magnetic field of induction B. Now a charge q is passed through the ring in a very small

time interval t . As a result the ring ultimately just becomes vertical. The value of g (acceleration due to

gravity is

22

qB

m r. Assume that friction is sufficient to prevent slipping and ignore any loss in energy.

Find the value of . [ ]

38. A current I flows in a long thin walled cylinder of

radius R. Pressure experienced by the wall of the

cylinder is 2

0

2 2,

I

n R where n is ________ .

y

X=0 X=L

x

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39. Charge Q is uniformly distributed on a thin insulating ring of mass m and radius r which is initially at rest

on a smooth horizontal surface. Now a cylindrical magnetic field B (radius )R r which is coaxial with the

ring is switched on. The angular velocity gained by will the ring will be .QB

m Find . [ ]

40.

The diagram shows a circuit having a coil of resistance R = 10Ω

and inductance L connected to a conducting rod PQ which can

slide on a perfectly conducting circular ring of radius 10cm with

its centre at ‘P’. Assume that friction and gravity are absent and

a constant uniform magnetic field of 5T exists as shown in the

figure. At t = 0, the circuit is switched on and simultaneously a

time varying external torque is applied on the rod so that it

rotates about P with constant angular velocity 40 rad/s. Find

magnitude of this torque (in μNm) when current reaches half of

its maximum value. Neglect the self-inductance of the loop

formed by the circuit.

---------------------------------------------------------------------- DAY-5 -----------------------------------------------------------------------

41. Two parallel vertical metallic rails AB and CD are separated by 1m. They

are connected at the two ends by resistances 1R and 2R as shown. A

horizontal metallic bar PQ of mass 0.2 kg slides without friction,

vertically down the rails under the action of gravity. There is uniform

horizontal magnetic field of 0.6T perpendicular to plane of the rails. It is

observed that when the terminal velocity is attained, the power dissipated

in 1R and 2R are 0.76 W and 1.2 W respectively. Find the terminal

velocity of bar in m/s. (g = 9.8 m/s2) [ ]

42. In the circuit shown in the figure, the key K1 was closed for a

long time and K2 was opened. At t = 0, key K1 is opened and

K2 is closed. If the charge of capacitor C1 is 3N C at the

instant energy stored in it is three times of energy stored in

the inductor, then N is________.

[ ]

A C

D B

R1

R2

P Q

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43. A non-conducting non-magnetic rod having circular cross-section of radius R

is suspended from a rigid support as shown in the figure. A light and small

coil of 300 turns is wrapped tightly at the left end of the rod where uniform

magnetic field B exists in vertically downward direction. Air of density hits

the half of the right part of the rod with velocity v inelastically as shown in

the figure. What should be current in clockwise direction (as seen from O) in

the coil so that rod remains horizontal? Give answer in mA, given

1/221 .

RBA

Lv

44. A block is attached to the ceiling by a spring that has a force constant k = 200 N/m. A

conducting rod is rigidly attached to the block. The combined mass of the block and the rod is m = 0.3 kg. The rod can slide without friction along two vertical parallel rails,

which are a distance l = 1 m apart. A capacitor of known capacitance C = 500 F is

attached to the rails by the wires. The entire system is placed in a uniform magnetic field

B = 20 T directed as shown. Find the angular frequency (in rad/sec) of the vertical oscillations of the block. Neglect the self-inductance and electrical resistance of the rod

and all wires.

45. A very long current carrying wire is placed along z-axis having current of magnitude 1i towards negative z-

axis. A semicircular wire of radius R and having current 2i is placed in x-y plane, such that line joining two

end points of the semicircular wire passes through long wire as shown in figure. Nearest distance of

semicircular wire from long wire is R. Net magnetic force on semicircular wire will be 0 1 2 ln2

i in . Find n.

[ ]

46. An -particle is accelerated by a potential difference of 104

V. Find the change in its direction of motion as

angle measured in degree if it enters normally in a region of thickness 0.1 m having transverse magnetic induction of 0.1 T.

[given mass of -particle = 6.4 10-27

kg]. [ ]

47. A capacitor of capacitance C

18

mH having initial charge Q0 connected to an inductor of inductance

18L mH at t = 0. Find the time (in milli second) after energy stored in electric field is three times

energy stored in magnetic field. [ ]

Q0

L + + + + – – – –

S

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48. A coil of inductance 1H and resistance 10 is connected to a resistance less battery of emf V50 at time

0t . The ratio of rate at which magnetic energy is stored in the coil to the rate at which energy is supplied

by the battery at .sec1.0t is 210x . Find the value of x. [ ]

(Given 37.01

e)

49.

In the circuit shown, the transformer is ideal

with turn ratio 1

2

5.

1

N

N The voltage of the

source is 300 .SV V The voltage measured

across the load resistance 100 LR is 50V.

Find the value of resistance R in the primary

circuit (in ) .

[ ]

50.

In the given circuit, initially switch 1S is closed and 2S and 3S are

open. After charging of capacitor, at t = 0, 1S is opened and 2S and

3S are closed. If the relation between inductance, capacitance and

resistance is 24L CR then find the time (in sec) after which

current passing through capacitor and inductor will be same.

(given ( 2) , 2 )R ln m L mH

[ ]

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Answer key : ALPS_ Physics – 2203

Magnetism, Electromagnetic Induction

Day 1

1 2 3 4 5 6 7 8 9 10

A A A C C D D C D C

Day 2

11 12 13 14 15 16 17 18 19 20

AC BD BC ACD BD ABD AB AB AD ACD

Day 3

21 22 23 24 25 26 27 28 29 30

B B C A A A B A A B

Day 4

31 32 33

A-p, q, s; B-p, q, r, s; C-p, q, s; D-q A-p, r, s; B-q; C-s; D-p, r, s A-r; B-p; C-q; D-s

34 35 36 37 38 39 40

A-q, r; B-p, s; C-p, r; D-q, s A-s; B-r; C-p; D-q 6 3 8 0.50 1250

Day 5

41 42 43 44 45 46 47 48 49 50

1 100 10 20 3 30 3 37 500 1

ALPS_ Physics - 2203 Magnetism, Electromagnetic Induction

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