# Magnetics - PDF

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```							MAGNETICS
MAGNETICS
Oersted’s experiment, Bio-Savert’s law, magnetic field due to straight wire, circular loop and solenoid, force on a moving charge in a uniform magnetic field (Lorentz force), forces and torques on currents in a magnetic field, force between two currents carrying wires, moving coil galvanometer and conversion to ammeter and voltmeter.

MAGNETOSTATICS
Bar magnet, magnetic field, lines of force, torque on a bar magnet in a magnetic field, earth’s magnetic field, para, dia and ferro magnetism, magnetic induction, magnetic susceptibility.

INITIAL STEP EXERCISE
1. A uniform electric field and a uniform magnetic field exist in a region in the same direction. An electron is projected with velocity pointed in the same direction. The electron will follow a (a) (c) 2. Straight path Helix path (b) (d) circular path Cycloidal path

An electron is injected into a uniform magnetic field with components of velocity parallel to and normal to the field direction. The path of the electron is a (a) (c) helix parabola (b) (d) circle straight line

3.

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If E and B represent the electric and magnetic fields respectively, this region of space may not have (a) (c) E = 0, B = 0 E ≠ 0, B = 0 (b) (d) E = 0, B ≠ 0 E ≠ 0, B ≠ 0

4.

A charged particle moving with a velocity v enters a uniform magnetic field B. The particle experiences the largest deflecting force when the angle between v and B is (a) (c) 00 900 (b) (d) 450 1800

5.

Ions of different momenta (p), having the same charge, enter normally a uniform magnetic field. The radius of the orbit of an ion is proportional to (a) (c) p p
2

(b) (d)

1/p 1/p2

6.

A proton and an α-particle, moving with the same kinetic energy, enter a uniform magnetic field normally. The radii of their circular paths will be in the ratio (a) (c) 1:1 1:2 (b) (d) 2:1 4:1

7.

Two particles X and Y having charge, after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular paths of radii R1 and R2 respectively. The ratio of the mass of X to that of Y is (a) (c) (R1 / R2)1/2 (R1 / R2)
2

(b) (d)

R2/R1 R1/R2

8.

A horizontal wire of length 10 cm and mass 0.3 g carries a current of 5A. The magnitude of the magnetic field which can support the weight of the wire is (g = 10 m/s2). (a) (c) 3 × 10–3T 3 × 10–4 T (b) (d) 6 × 10–3 T 6 × 10–4 T

9.

A conducting circular loop of radius r carries a constant current i. It is placed in a uniform magnetic field B such that B is perpendicular to the plane of the loop. The magnetic force, torque and potential energy of the loop is respectively (a) (c) 0, 0, –iπr2B Bir, 0, –iπr2B (b) (d) 0, 0, 0 2Bir, 0, –iπr2B

10.

In a moving coil galvanometer the current i is related to the deflection θ as i = θn, where n is a constant. The value of n is (a) (c) 1 ½ (b) (d) –1 –½

11.

A square coil of side a carries a current I. The magnetic field at the centre of the coil is

(a)

µ0 I aπ
µ0 I 2aπ

(b)

2µ 0 I aπ 2 2µ 0 I aπ

(c) 12.

(d)

Two circular coils have number of turns in the ratio 1 : 2 and radii in the ratio 2 : 1. If the same current flows through them, the magnetic fields at their centers will be in the ratio (a) (c) 1:1 2:1 (b) (d) 1:2 1:4

13.

A charged particle enters a magnetic field such that the direction of initial velocity is different from the direction of the field. Which of the following characteristics of the particle doesn’t change with time? (a) (b) (c) (d) momentum kinetic energy acceleration direction of motion

14.

The magnetic field inside a current carrying toroidal solenoid is B. If its radius is doubled and the current through it is also doubled, the magnetic field inside the solenoid will be (a) (c) B/2 2B (b) (d) B 4B

15.

A long solenoid has 20 turns/cm. The current necessary to produce a magnetic field of 20 millitesla inside the solenoid is approximately (a) (c) 1A 4A (b) (d) 2A 8A

16.

Two identical coils have a common centre and their planes are at right angles to each other. They carry equal currents. If the magnitude of the magnetic field at the centre due to one of the coils is B then that due to the combination is

(a) (c) 17.

B B/√2

(b) (d)

√2B 2B

A current of 1 A is flowing in the sides of an equilateral triangle of side 4.5 × 10–2 m. The magnetic field at the centroid of the triangle is (a) (c) 2 × 10–5 T 8 × 10 T
–5

(b) (d)

4 × 10–5 T 1.2 × 10–4 T

18.

In the given figure the straight parts of the wire are very long. The magnetic induction at O is (a) (b) (c) (d)

µ0 I µ0 I + 4r 2πr out of the page µ0 I µ0 I + 4r 4πr out of the page µ0 I µ0 I + 4r 4πr into the page µ0 I µ0 I + 4r 2πr into the page

19.

A long thin wire is bent as shown in the figure. The radius of the semicircular part is r metres. If a current of I ampere flows through the wire, then the magnetic induction at O in tesla is

(a)

µ0 I ⎛ 1 ⎞ ⎜1 + ⎟ 2r ⎝ π ⎠ out of the page µ0 I ⎛ 1 ⎞ ⎜1 + ⎟ 2r ⎝ π ⎠ into the page µ0 I ⎛ 2 ⎞ ⎜1 + ⎟ 4r ⎝ π ⎠ out of the page µ0 I ⎛ 2 ⎞ ⎜1 + ⎟ 4r ⎝ π ⎠ into the page

(b)

(c)

(d)

20.

In the given loop, the magnetic field at the centre O is

(a)

µ 0 I ⎛ r1 + r2 ⎞ ⎟ ⎜ 4 ⎜ r1r2 ⎟ ⎠ ⎝

out of the page

(b)

µ 0 I ⎛ r1 + r2 ⎞ ⎟ ⎜ 4 ⎜ r1r2 ⎟ ⎠ ⎝ µ 0 I ⎛ r1 − r2 ⎞ ⎟ ⎜ 4 ⎜ r1r2 ⎟ ⎠ ⎝ µ 0 I ⎛ r1 − r2 ⎞ ⎟ ⎜ 4 ⎜ r1r2 ⎟ ⎠ ⎝

into the page

(c)

out of the page

(d)

into the page

21.

A charged particle enters a region where a uniform electric field E and a uniform magnetic field B exist. If E and B are perpendicular to each other and also perpendicular to the velocity u of the particle, then the particle will move undeviated if u equals (a) (c) B/E EB (b) (d) E/B E2/B2

22.

To make the field radial in a moving coil galvanometer (a) (b) (c) (d) the number of turns in the form of increased magnet is taken in the form of horse-shoe poles are cylindrically cut coil is wound on aluminium frame

23.

A proton and an α-particle enter a uniform magnetic field perpendicularly, with the same speed. If the proton takes 25 microseconds to make 5 revolutions, the periodic time for the α-particle would be (a) (c) 50 µs 10 µs
–12

(b) (d)

25 µs 5 µs

24.

If a particle of charge 10 C moving along the x-direction with a velocity 105 m/s experiences a force of 10–10 N in y-direction, then the minimum magnetic field is (a) (b) (c) (d) 6.25 × 103 T in the positive z-direction 10–15 T in the negative z-direction 10–3 T in the positive z-direction 10–3 T in the negative z-direction

25.

A vertical wire carrying a current in the upward direction is placed in a horizontal magnetic field directed towards north. The wire will experience a force towards (a) (c) North East (b) (d) South West

26.

If a bar magnet moment 80 units be cut into two halves of equal lengths, the magnetic moment of each half will be (a) (c) 80 units 40 units (b) (d) 60 units 20 units

27.

Magnetic lines of force (a) cannot intersect at all

(b) (c) (d) 28. (a) (b) (c) (d) 29.

intersect at infinity intersect within the magnet intersect at the neutral points start from the north pole and end at the south pole run continuously through the bar and outside emerge in circular paths from the middle of the bar are produced only at the north pole like rays of light from a bulb

In the case of a bar magnet, the lines of magnetic induction

The period of oscillation of a magnet in a vibration magnetometer is 2s. The period of oscillation of a magnet whose magnetic moment is four times that of the first magnet is (a) (c) 1s 8s (b) (d) 5s 0.5 s

30.

The time period of oscillation of a freely suspended magnet is 4 s. It is broken in length into two equal parts and one part is suspended in the same way, its time period will be (a) (c) 4s 0.5 s (b) (d) 2s 0.25 s

31.

At a certain place the horizontal component of earth’s magnetic field is √3 times the vertical component. The angle of dip at that place is (a) (c) 750 45
0

(b) (d) (b) (d)

600 300 300 900

32.

At magnetic poles the angle of dip is (a) (c) 450 00

33.

At a certain place, the angle of dip is 300 and the horizontal component of earth’s magnetic field is 0.5 T. The earth’s total magnetic field is (a) (c)

√3
1/√3 zero angle of dip

(b) (d)

1 none of these

34.

Isogonic lines on a magnetic map have (a) (b) (c) (d) zero angle of declination the same angle of dip the same angle of declination low susceptibility and low retentivity high susceptibility and high retentivity high susceptibility and low retentivity low permeability and high retentivity

35.

Electromagnets are made of soft iron because soft iron has (a) (b) (c) (d)

36.

A bar magnet of magnetic moment M is cut into two parts of equal length. The magnetic moment of either part is (a) (c) M M/2 (b) (d) 2M zero

37.

A magnetic needle suspended by a silk thread is vibrating in the earth’s magnetic field. If the temperature of the needle is increased by 5000C, then (a) the time period decreases

(b) (c) (d) 38. (a) (b) (c) (d) 39. (a) (c) 40.

the time period remains unchanged the time period increases the needle stops vibrating dipped in water dipped in oil brought near a piece of iron strongly heated air steel (b) (d) soft iron Cu-Ni alloy

All the magnetic materials lose their magnetic properties when

Which of the following is most suitable for the core of an electromagnet?

If a diamagnetic solution is poured into a U-type and one arm of this U-tube placed between the poles of a strong magnet, with the meniscus in a line with the field, then the level of the solution will (a) (c) rise (b) fall remain as such oscillate slowly (d)

41.

The time period of oscillation of a bar magnet suspended horizontally along the magnetic meridian is T0. If this magnet is replaced by another magnet of the same size and pole strength, but with double the mass, the new time period will be (a) (c) T0/2 (b) (d) T0/√2 2T0

√2T0

42.

Magnet permeability is maximum for (a) (b) (c) (d) diamagnetic substances paramagnetic substances ferromagnetic substances all of these

43.

At the magnetic north pole of the earth, the value of the horizontal component of earth’s magnetic field and the angle of dip are respectively (a) (b) (c) (d) zero, maximum maximum, minimum maximum, maximum minimum, minimum permeability of the material susceptibility of the material retentivity of the material energy dissipated per cycle high retentivity, low coercivity low retentivity, high coercivity low retentivity, low coercivity high retentivity, high coercivity 00 (b) 300

44.

The area of the B-H hysteresis loop is an indication of the (a) (b) (c) (d)

45.

The material of a permanent magnet has (a) (b) (c) (d)

46.

A dip circle is at right angles to the magnetic meridian. The apparent dip is (a)

(c) 47.

600

(d)

900

A hollow cylinder of radius r carries a current I. Let the magnetic field inside the cylinder is B1 and outside the cylinder is B2. Then (a) (c) B1 = 0, B2 ≠ 0 B1 = 0, B2 = 0 (b) (d) B1 ≠ 0, B2 ≠ 0 B1 ≠ 0, B2 = 0

48.

A solid cylinder of radius r carries a current I. Let the magnetic field from the axis of the cylinder is B. Which of the following graph will represent the variation of B with the distance (x) from the axis of the cylinder?

(a)

(b)

(c)

(d)

Solutions:

1. 7. 13. 19.

a c b c

2. 8. 14. 20.

a b c b

3. 9. 15. 21.

c a d b

4. 10. 16. 22.

c a b c

5. 11. 17. 23.

a d b c

6. 12. 18. 24.

a d b d

25. 31. 37. 43.

d d c a

26. 32. 38. 44.

c d d d

27. 33. 39. 45.

a c b d

28. 34. 40. 46.

b d b d

29. 35. 41. 47.

a c c a

30. 36. 42. 48.

b c c c

FINAL STEP EXERCISE

1. A potential difference of 600 V is applied across the plates of a parallel plate capacitor. The separation between the plates is 3 mm. A magnetic field also exists between the plates. An electron projected parallel to the plates as shown with a speed of 2 × 106 m/s moves undeflected between the plates. The magnitude and direction of the magnetic field is (a) (b) (c) (d) 0.2 T, into the page 0.2 T, out of the page 0.1 T, into the page 0.1 T, out of the page

2.

i A particle of charge +q and mass m moving under the influence of a uniform electric field Eˆ and a ˆ follows a trajectory from P to Q as shown in the figure. The velocities at P uniform magnetic field Bk ˆ ˆ and Q are vi and − 2 vj . Which of the following statements is incorrect?

(a)

3 ⎛ mv2 ⎞ ⎟ E= ⎜ 4 ⎜ qa ⎟ ⎠ ⎝ 3 ⎛ mv3 ⎞ ⎟ ⎜ 4⎜ a ⎟ ⎠ ⎝

(b) (c) (d)

Rate of work done by the electric field at P is

Rate of work done by the electric field at P is zero. Rate of work done by both the fields at Q is zero.

3.

A long horizontally fixed wire carries a current of 100 A. Directly above and parallel to it is another wire carrying a current of 20 A and weighing 0.04 N/m. What should be the separation between the two wires so that the upper wire is just supported by magnetic repulsion?

(a) (c) 4.

1 cm 3 cm

(b) (d)

2 cm 4 cm

A charge q coulomb is circulating in an orbit of radius r metres making n revolutions per second. The magnetic field produced at the centre of the circle in N/Am is (a) (c)

2πq × 10−7 nr 2πnq × 10−7 r

(b) (d)

2πq × 10−7 r
2πrn ×10 −7 q

5.

In the figure AB is a long straight wire carrying a current of 20 A and CDFG is a rectangular loop of size 20 cm × 9 cm carrying a current of 10 A. The edge CG is parallel to AB, at a distance of 1 cm from it. The force exerted on the loop by the magnetic field of the wire is (a) (b) (c) (d) 3.6 × 10–4 N towards left 3.6 × 10–4 N towards right 7.2 × 10–4 towards right 7.2 × 10–4 towards left

6.

In the figure x, y and z are long straight wires. The magnetic force on 25 cm length of y is (a) (b) (c) (d) 2 × 10–4 N towards right 4 × 10–4 N towards right 2 × 10–4 N towards left 4 × 10–4 towards left

7.

A circular loop of mass m and radius r lies on a horizontal table (xy-plane). A uniform magnetic field is applied parallel to the x-axis. The current I that should flow in the loop so that it just tilts about one point on the table is

(a) (c)

mg πr 2 B mg πrB

(b) (d)

mg 2πrB
πrB mg

8.

A charged particle having kinetic energy E enters normally a region of uniform magnetic field between two plates P1 and P2 as shown in the figure. If the particle just misses hitting the plate P2, then the magnetic field B in the region between the plates is (a)

mE 2qd

(b)

2mE qd

(c)

mE 2qd

(d)

2mE qd

9.

A magnet is suspended in such a way that it oscillates in the horizontal plane. It makes 20 oscillations per minute at a place where the dip angle is 300 and 15 oscillations per minute at a place where the dip angle is 600. The ratio of earth’s total magnetic fields at the two places is (a) (c) 3√3 : 8 4:9 (b) (d) 2√3 : 9 16 : 9√3

10.

The magnetic field at a point A on the axis of a small bar magnet is equal to the field at a point B on the equator of the same magnet. The ratio of the distances of A and B from the centre of the magnet is (a) (c) 2–3 23 (b) (d) 2–1/3 21/3

11.

A magnetic needle lying parallel to a magnetic field requires W units of work to turn it through 600. The torque required to maintain the needle in this position is

(a) (c)

√3 W W

(b) (d)

3 W 2
2W

12.

A bar magnet of length 10 cm and having pole strength equal to 10–3 A-m is kept in a magnetic field (B) of 4π × 10–3 tesla. It makes an angle of 300 with the direction of B. The torque acting on the magnet is (a) (c) 2π × 10–7 Nm 0.5 Nm (b) (d) 2π × 10–5 Nm 0.5 × 102 Nm

13.

A tangent galvanometer has a coil with 50 turns and radius equal to 4 cm. A current of 0.1 ampere is passing through it. The plane of the coil is set parallel to the earth’s magnetic meridian. If the value of the horizontal component of earth’s magnetic field is 7 × 10–5 tesla and µ = 4π × 10–7 Wb/Am, then the deflection in the galvanometer coil will be (a) (c) 450 50.70 (b) (d) 48.20 52.70

14.

A short magnet of moment 6.75 Am2 produces a neutral point on its axis. If the horizontal component of earth’s magnetic field is 5 × 10–5 Wb/m2, then the distance of the neutral point from the centre of the magnet is (a) (c) 10 cm 30 cm (b) (d) 20 cm 40 cm

15.

A wire of given length is folded into a circular coils of constant radius. A constant current is flowing through the loop. The magnetic field produced at the centre of the coil is directly proportional to the number of turns as nα. The value of α is (a) (c) –1 2 (b) (d) 1 3

16.

In the above problem the magnetic dipole moment of the loop depends on number of turns as nα . The value of α is (a) (c) –1 2 (b) (d) 1 3

Solutions:

1. 7. 12.

d c b

2. 8. 14.

c d c

3. 9. 15.

d d c

4. 10. 16.

c d a

5. 11.

d a

6. 12.

b a

ANALYSIS
1. A particle of charge –16 × 10–18 coulomb moving with velocity 10 ms–1 along the x-axis enters a region where a magnetic field of induction B is along the y-axis, and an electric field of magnitude 104V/m is along the negative z-axis. If the charged particle continues moving along the x-axis, the magnitude of B is (a) (c) [Ans. : c] 1016Wb/m2 10 Wb/m
3 2

(b) (d)

10–3Wb/m2 105Wb/m2

2.

A thin rectangular magnet suspended freely has a period of oscillation equal to T. Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely T′ in the same field. If the period of oscillation is T’, the ratio T is (a) (c) [Ans. : d] 2 1/2√2 (b) (d) 1/4 1/2

3.

A magnetic needle lying parallel to a magnetic field requires W units of work to turn it through 600. The torque needed to maintain the needle in this position will be

(a) (c) [Ans. : c] 4.

3 W 2 √3 W

(b) (d)

2W W

The magnetic lines of force inside a bar magnet (a) (b) (c) (d) [Ans. : c] depend upon the area of cross-section of the bar magnet are from south-pole to north-pole of the magnet are form north-pole to south-pole of the magnet do not exist

5.

Curie temperature is the temperature about which (a) (b) (c) (d) [Ans. : c] a ferromagnetic material becomes diamagnetic a paramagnetic material becomes ferromagnetic a ferromagnetic material becomes paramagnetic a paramagnetic material becomes diamagnetic

6.

A particle of mass M and charge Q moving with velocity describes a circular path of radius R when subjected to a uniform transverse magnetic field of induction B. The work done by the field when the particle completes one full circles is

(a)

BQ2πR

(b)

BQv2πR

(c)

⎛ Mv 2 ⎞ ⎜ ⎟ ⎜ R ⎟2 π R ⎠ ⎝

(d)

zero

[Ans. : d]

1.

A current i ampere flows along an infinitely long straight thin walled tube then the magnetic induction at any point inside the tube is (a) (c) infinite (b) zero

2i tesla r

[Ans. : b] 3. The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is 54 µT. What will be its value at the centre of the loop? (a) (c) [Ans. : a] 4. Two long conductors, separated by a distance d carry current l1 and l2 in the same direction. They exert a force F on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to 3d. The new value of the force between them is (a) (c) [Ans. : c] 5. The length of a magnet is large compared to its width and breath. The time period of its oscillation in a vibration magnetometer is 2 s. The magnet is cut along its length into three equal parts and three parts are then placed on each other with their like poles together. The time period of this combination will be (a) (c) [Ans. : b] 6. The materials suitable for making electromagnets should have (a) (b) (c) (d) [Ans. : b] 7. One conducting U tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field B is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed V, then the emf induced in the circuit in terms of B, l and V where l is the width of each tube, will be high retentivity and high coercivity low retentivity and low correcivity high retentivity and low coercivity low retentivity and high coercivity 2s 2√3 s (b) (d) 2/3 s 2/√3 s –2F –2F/3 (b) (d) F/3 –F/3 250 µT 125 µT (b) (d) 150 µT 75 µT

(a) (c) [Ans. : b] 8.

zero BlV

(b) (d)

2 BlV –BlV

Two thin, parallel wires, separated by a distance‘d’ carry a current of ‘i’ A in the same direction. They will (a) (b) (c) attract each other with a force of µ0i2 / (2πd2) repel each other with a force of µ0i2 / (2πd) attract each other with a force of µ0i2 / (2πd)

(d) [Ans. : c] 9.

repel each other with a force of µ0i2 / (2πd2)

Two concentric coils each of radius equal to 2π cm are placed at right angle to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic induction in Weber/m2 at the centre of the coils will be (µ0 = 4π × 10–7 Wb / A . m) (a) (c) 5 × 10–5 12 × 10
–5

(b) (d)

7 × 10–5 10–5

[Ans. : b] 10. A charged particle of mass m and charge q travels on a circular path of radius r that is perpendicular to a magnetic field B. The time taken by the particle to complete one revolution is (a) (c) [Ans. : b] 11. A magnetic needle is kept in a non-uniform magnetic field. It experiences (a) (b) (c) (d) [Ans. : d] 12. A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity then (a) (b) (c) (d) [Ans. : c] it will turn towards right of direction of motion it will turn towards left of direction of motion its velocity will decrease its velocity will increase a force and a torque a force but not a torque a torque but not a force neither a force nor a torque

2πqB m 2πmq B

(b) (d)

2πm qB 2πq 2 B m

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