CHAPTER-3

MOVING CHARGES AND MAGNETIC FIELDS

1-MARK NCERT QUESTIONS
1. State two factors on which the sensitivity of a moving coil galvanometer depends.
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2.
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The force F experienced by a particle of charge q moving with velocity v in a magnetic field B is given by F = q v ´ B . which pair of vectors is always at
right angles to each other?
3. What shunt? Give its S.I. units.
4. Under what condition, an electron moving through a magnetic field experiences maximum force?
5. Consider the circuit shown here where APB and AQB are semi-circles. What will be the magnetic field at the centre C of the circular loop?

6. Define the term magnetic moment.

7. Under what condition is the force acting on a charge moving through a uniform magnetic field, minimum?
8. A current is set up in a long copper pipe Is there a magnetic field (i) inside (ii) outside the pipe?
9. What is the nature of the magnetic field in a moving coil galvanometer?
10. An electron beam is moving vertically upwards. If it passes through a magnetic field, which is directed, from south to north in a horizontal plane, then in
which direction will the beam be deflected?
11. In a certain arrangement a proton does not get deflected while passing through a magnetic field region. Under what condition is it possible?
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12. The force F experienced by a particle of charge q moving with velocity v in a magnetic field B is given by F = q v ´ B . Of these, name the pairs of
vectors which are always at right angles to each other.
13. An electron and a proton moving with the same speed enter the same magnetic field region at right angles to the direction of the field. For which of the
two particles will the radius of circular path be smaller?
14. Name the physical quantity whose S.I. unit is Wb-m–2. Is it a scalar or a vector quantity?
15. Equal currents I are flowing through two infinitely long parallel wires. What will be the magnetic field at a point mid-way when the currents are flowing
in the same direction?
17. How will the magnetic field intensity at the centre of a circular coil carrying current change, if the current through the coil is doubled and the radius of
the coil is halved?
18. State two properties of the material of the wire used for suspension of the coil in a moving coil galvanometer.
19. What is the advantage of using radial magnetic field in a moving coil galvanometer
20. An anuneter and milli-ammeter are converted from the same galvanometer. Out of the two, which current measuring instrument has higher resistance?
21. Which one of the following will experience maximum force, when projected with the same velocity ‘v’ perpendicular to the filed ’B’: (i) a -particle. and
(ii) b -particle?
22. Which one of the following will describe the smallest circle when projected with the same velocity ‘v’ perpendicular to the magnetic field ‘B’: (i) a -
particle. and (ii) b -particle?

23. Which one of the following will have minimum frequency of revolution, when projected with the same velocity (v) perpendicular to the magnetic field
‘B’: (i) a -particle. and (ii) b -particle?

24. Write expression for Lorentz force acting on a charged particle?

25. Is any work done by a magnet field on a moving charge? Why?
2-MARKS
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26. Estimate the torque acting on a closed current loop placed in magnetic field B .
27. Derive an expression for the magnetic field intensity at a point due to a current carrying straight wire of infinite length.
28. Explain why two straight parallel metallic wire carrying current in opposite directions repel each other.
29. What is the basic difference between magnetic lines and electric lines of forces? Write Gauss ‘Law on magnetism.
30. Write down the expression for the force on a current carrying conductor placed in a magnetic field. State Fleming’s Left Hand Rule.
31. Derive an expression for the magnetic field at the centre of a circular current carrying coil.
32. In the figure, the straight wire AB is fixed while the loop is free to move under the influence of the electric currents flowing in them. In which direction
does the loop begin to move? Give reason for your answer.
33. How can a galvanometer of resistance G be converted into a voltmeter to read maximum potential difference of ‘V’ volts? Support your answer with
related mathematical expression.
34. What is solenoid? Give the magnitude of magnetic field developed at a point well inside a solenoid c allying current.
35. In what respect a current carrying wire differ from a wire which carry no current?
36. Why do two straight conductors carrying current in opposite direction repel each other?
37. What is the source of magnetic field?
38. How does a voltmeter differ from ammeter?
39. A charge q moving in a straight line is accelerated by a potential difference V. It enters a uniform magnetic field B perpendicular to its path. Deduce in
terms of V an expression for the radius of the circular path in which it travels.
40. A current is considered a magnetic dipole. Explain.
41. Define the S.I. unit of magnetic field. Under what condition does a moving charge in uniform magnetic field experience maximum force?
42. Define the S.I. unit of magnetic field. Under what condition does a moving charge in a uniform magnetic field experiences zero force?
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43. Define S.I. unit of magnetic field in the expression for Lorentz force = F = q V ´ B , which two pairs of vectors are always perpendicular to each other?
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44. Twelve wires of equal length are connected in the form of a skeleton-cube which is moving with a velocity V in the direction of a magnetic field B . Find
the e.m.f. in each arm of the curb.
45. Define the S.I. unit of magnetic field. “A charge moving at right angles to uniform magnetic field does not undergo change in kinetic energy.” Why?
46. A stream of electrons travelling with speed ‘v’ m s at right angles to a uniform magnetic field ‘B’ is deflected in a circular path of radius ‘r’. Prove that
e v
=
m rB
47. What is the magnetic moment associated with a coil of 1 turn, area of cross-section 10–4 m2. carrying a current of 2A?
48. The coil of a galvanometer has a resistance of 100 ohm. It shows full scale deflection for a current of 5 × 10–4 A. How will you convert into a voltmeter to
read a maximum p. d. of 5V?
49. A beam of alpha particles and of the protons of the same velocity v, enter a uniform magnetic field at right angles to the field lines. The particles describe
circular paths. What is the ratio of the radii of these two circles?
50. A galvanometer having a coil resistance of 100 W gives full scale deflection when a current of 1 mA is passed through it. Calculate the value of resistance
required to convert it into an ammeter of the range of 1 A.
51. Calculate the value of the resistance needed to convert a galvanometer of resistance 100 W which gives a full scale deflection for a current of 5 mA. into a
voltmeter of 0 – 10 V range.
52. Calculate the value of the resistance needed to convert a galvanometer of resistance 120 W , which gives a full scale deflection for a current of 5 mA, into a
voltmeter of 0-50 V range.
53. An electron of kinetic energy 25 keV moves perpendicular to the direction of a uniform magnetic field of 0.2 millitesla. Calculate the time period of
rotation of the electron in the magnetic field.
54. An electron in an atom revolves around the nucleus in an orbit of radius 0.53 Å . Calculate the equivalent magnetic moment if the frequency of revolution
of electron is 6.8 × 109 MHz.
55. Calculate the value of resistance needed to convert a galvanometer of resistance 100 W which gave a full scale deflection for a current of 5 mA into a
voltmeter of 0-10 V range.
56. If the current sensitivity of a moving coil galvanometer is increased by 20%. its resistance also increases by 1.5 times. How will the voltage sensitivity of a
galvanometer be affected?
57. A coil of 200 turns has a cross-sectional area 900 mm2. It carries a current of 2 ampere. The plane of the coil is perpendicular to a uniform magnetic field of
0.5 T. Calculate (i) the magnetic moment of the coil and (ii) the torque acting on the coil.
3-MARKS
58. Explain how will you convert a galvanometer into an ammeter of a given range.
59. Derive an expression for the torque on a rectangular coil of area A, carrying a current I placed in a magnetic field B. The angle between the direction of B
q
and the vector perpendicular to the plane of the coil is .
60. A moving coil galvanometer consists of a rectangular coil of N turns, each of area A, suspended in a radial magnetic field of flux density B. Derive the
expression for the torque on the coil, when current I passes through it. Draw suitable labelled diagram.
61. A straight wire carries a current of 3A. calculate the magnitude of the magnetic field at a point 10 cm away from the wire. Draw a diagram to show the
direction of the magnetic field.
62. Explain how will you convert galvanometer into a voltmeter to read a maximum potential of ‘V’ volts. Can one use a voltmeter to measure the e.m.f. of a
cell? Justify your answer.
63. Derive the expression for the force between two infinitely long parallel straight wires carrying current in the same direction. Hence define one ampere.
64. Derive an expression fro the force experienced by a current carrying straight conductor placed in a magnetic field. Under what condition is this force
maximum?
65. A proton and an a -particle of the same K.E., in nun move through a uniform magnetic field B, in a plane normal to the field. Compare the radii of the
paths of the two particles.
66. Explain with reason, in which direction does the current loop KLMN move, when kept near an infinitely long straight wire, carry current as shown in
figure below:

67. Using Biot-Savart law, derive an expression for the magnetic field at the centre of a circular coil of radius ‘r’ having ‘N’ number of turns. Indicate the
direction of the magnetic field.
68. A proton and an alpha particle of the same velocity enter in turn a region of uniform magnetic field acting in a plane perpendicular to the magnetic field.
Deduce the ratio of the radii of the circular paths described by the particles. Explain why the kinetic energy of the particle after emerging from the
magnetic field, remains unaltered.
69. Describe the motion of a charged particle in a uniform magnetic field. Obtain an expression for the radius of the path of the charged particle moving
perpendicular to uniform magnetic field. Show that the time taken to complete one revolution by the particle is independent of its speed.
70. What is meant by radial magnetic field? A moving coil galvanometer consisting of a rectangular coil of N turns, each of area A is suspended in a radial
magnetic field of flux density b. With the help of labeled diagram, derive the expression for the torque on the coil when a current I pass through it.
71. A particle with charge ‘q’ moving with a velocity ‘v’ moving in the plane of the paper enters a uniform magnetic field ‘B’, acting perpendicular to the
plane of the paper. Deduce an expression for the time period of the charge, as it moves in a circular path in the field. Why does the kinetic energy of the
charge not change, while moving in the magnetic field?
72. How can a moving coil galvanometer be converted into an ammeter? To increase the current sensitivity of a moving coil galvanometer by 50%. its
resistance is increased so that the new resistance becomes twice its initial resistance. By what factor does its voltage sensitivity change?
73. A charged particle of mass ‘m’ and ‘q’ moving at uniform velocity ‘V’, enters a uniform magnetic field ‘B’ acting normal to the plane of the paper. Deduce
expression for the (i) radius of the circular path in which it travels, (ii) kinetic energy of the particle (assuming V ! C ). Why does the kinetic energy of
the charge not change, when moving through the magnetic field?
74. Write the expression for Biot-Savart law for the magnetic field due to a small current carrying element. Using this expression calculate the magnetic field
at the centre of current carrying circular coil of radius ‘r’ having ‘n’ number of turns.
75 Write the expression for Biot-Savart’s law for the magnetic field due to a small current carrying element. Using this expression, calculate the magnetic
field intensity at a point on the axis of a circular current carrying conductor.
76. State Biot-Savart law. Use it to obtain the intensity of magnetic field at a point due to a long straight current carrying wire.
77. An electron moving with a speed of 108 m/s enters a magnetic field of 5 × 10–3 T in a direction perpendicular to the field. Calculate
(a) radius of path (b) frequency of revolution of electron.
78. A chamber is maintained at 5 × 10–3 T. An electron enters it with a speed 5 × 10–7 m/s perpendicular to field. Calculate (i) radius of path (ii) frequency of
revolution of electron.
79. An electron being accelerated through 100 V enters a uniform magnetic field of 0.004 T perpendicular to direction of motion. Calculate the radius of path
discussed by electron.
80. A current of 7 A is flowing in a plane circular coil of radius 1 cm having no. of turns 100. The coil is placed in a uniform magnetic field of 0.2 wb/m2. If
the coil is free to rotate, which orientation would correspond to (i) stable equilibrium (ii) unstable equilibrium? Calculate P.E. in two cases.
81. A galvanometer with a coil of resistance 12.0 ohms shows frill scale deflection fro a current of 50 mA. How will you convert the galvanometer into (a) an
ammeter of range 0 to 0.5 A (b) a voltmeter of range 0 to 10 V?
82. A current of 5.0 A flows through each of two parallel long wires. The wires are 2.5 cm apart. Calculate the force acting per unit length of each wire. What
will be the direction of force if both currents flow in same direction?
83. A voltmeter reads 5.0 V at full scale deflection and is graded according to its resistance per volt at full scale deflection as 20000 W / V . How will you
convert it into a voltmeter that reads 15 V at full scale deflection?
84. In a galvanometer there is a deflection of 10 divisions per mA. The internal resistance of the galvanometer is 78 W . If a shunt of 2 W is connected to the
galvanometer and there are 75 divisions in all on the scale of the galvanometer, calculate the maximum current which the galvanometer can read.
85. A long straight wire AB carries a current of 4 A. Am proton P travels at 4 × 106 m/s, parallel to the wire, 0.2 m from it and in a direction opposite to the
current as shown in the figure. Calculate the force which the magnetic field of current exerts on the proton. Also specify the direction of the force.

86. A current carrying conductor PQ of length 1 m, mass 4.4 × 10–3 kg and resistance 50 milli-ohm is kept in a uniform magnetic field of 1.8 m T as shown in
the figure.
(i) State the rule for finding the direction of the force experienced by the conductor in the magnetic field. Indicate the direction of the force on PQ.
(ii) Calculate the potential difference ‘V‘ that must be applied to the conductor PQ so that it remains in equilibrium in the magnetic field.

87. Find the force on a wire (of negligible mass) of length 4.0 cm placed inside a solenoid near its centre, making an angle of 60° with its axis. The wire carries
a current of 12 A and magnetic field due to solenoid has a magnitude of 0.25 T. Find also the direction of the force experienced by the wire.
5-MARKS
88. Explain the theory of cyclotron. Why is cyclotron not suitable for accelerating electrons?
89. Explain with the help of a labelled diagram the underlying principle, construction and working of cyclotron.
90. Derive a mathematical expression for the force per unit length acting on each of the two straight parallel metallic conductors carrying current in the same
direction and kept near each other. Why do such current carrying conductors attract each other?
91. Derive a mathematical expression for the force acting on a current carrying straight conductor kept in a magnetic field. State the rule used to determine
the direction of this force.
92. Derive an expression for magnetic field due to a long straight conductor.
93. Explain Biot-Savart law. Obtain an expression for the magnetic field at a point situated at x meter away from centre of a circular coil of N turns and for r
meter radius carrying a current of I ampere.
94. Find an expression for magnetic field at the center of a circular coil carrying current.
95. Prove that two parallel conductors of infinite lengths, carrying currents in the same direction attract each other. Deduced the expression for the force per
unit length, experienced by each conductor.
96. Explain with the help of a labelled diagram the principle, construction and working of a cyclotron.
97. Prove that two parallel conductors carrying current in the opposite directions repel each other. Hence deduce an expression for the force per unit length
experienced by each conductor.
98. State Biot-Savart law. Using Biot-Savart law, derive an expression for the magnetic field at the centre of circular coil of numbers of turns ‘N’ radius ‘r’
carrying a current ‘i’.
A semi-circular arc of radius 20 cm carries a current of 10 A. Calculate the magnitude of the magnetic field at the centre of the arc.

ANSWERS
47. 2×10–4 Am2

48. Series resistance R = 9900 W

49. 2:1

50. 0.1 W

53. 1.79 × 10–7 s

54. 9.6 × 10–24 Am2

56. 80% of original value

57. (i) 36 × 10–2 Am2 (ii) zero

77. (a) 0.144 m (b) 1.40 × 108 Hz

79. r = 8.43 × 10–3 m

80. (i) zero (ii) 0.044 J

82. 10–4 M
83. By using R = 2 ´ 104 W in series
84. I = 0.3 A
85. 25.6 × 10–19 N away from the wire
86. V = 1.2 volt
87. F = 0.104 N
98. 1.57 × 10–5 Tesla