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10 1. Write the relation for the force acting on a charge carrier q moving with velocity through a magnetic field in vector notation. Using this relation, deduce the conditions under which this force will be (i) maximum (ii) minimum. 2. Draw a labelled diagram of a moving coil galvanometer. State the principle on which it works. Deduce an expression for the torque acting on a rectangular current carrying loop kept in a uniform magnetic field. Write two factors on which the current sensitivity of a moving coil galvanometer depends. 3. State BiotSavart law. Use it to derive an expression for the magnetic field at the centre of a circular loop of radius R carrying a steady current I. Sketch the magnetic field lines for such a current carrying loop. 4. An electron is moving along +ve x axis in the presence of uniform magnetic field along +ve y axis. What is the direction of the force acting on it? 5. A galvanometer has a resistance of 30Ω. It gives full scale deflection with a current of 2mA. Calculate the value of the resistance needed to convert it into an ammeter of range 00.3A. 6. Explain, with the help of a labelled diagram, the principle and construction of a cyclotron. Deduce an expression for the cyclotron frequency and show that it does not depend on the speed of the charged particles. 7. State the principle of working of a cyclotron. Write two uses of this machine.

11 8. With the help of a neat and labelled diagram, explain the underlying principle and working of a moving coil galvanometer. What is the function of: (i) uniform radial field (ii) soft iron core in such a device? 9. Derive a mathematical expression for the force per unit length experienced by each of the two long current carrying conductors placed parallel to each other in air. Hence define one ampere of current. Explain why two parallel straight conductors carrying current in the opposite direction kept near each other in air repel? 10. State the Biot Savart law for the magnetic field due to a current carrying element. Use this law to obtain formula for magnetic field at the centre of a circular loop of radius R carrying a steady current I. Sketch the magnetic field lines for a current loop clearly indicting the direction of the field. 11. Write an expression for the force experienced by a charged particle moving in a uniform magnetic field B. 12. Derive an expression for the torque acting on a loop of N turns, area A, carrying current i, when held in a uniform magnetic field. With the help of circuit, show how a moving coil galvanometer can be converted into an ammeter of given range. Write the necessary mathematical formula. 13. How do you convert a galvanometer into an ammeter? Why is an ammeter always connected in series? 14. Under what conditions is the force acting on a charge moving through a uniform magnetic field minimum? 15. Under what condition does an electron moving through a magnetic field experience maximum force? 16. Depict the magnetic field lines due to two straight, long, parallel conductors carrying currents I 1 and I 2 in the same direction. Hence deduce an expression for the force acting per unit length on one conductor due to the other is this force attractive or repulsive? 17. Figure shows a rectangular current carrying loop placed 2cm away from a long, straight, current carrying conductor. What is the direction and magnitude of the net force acting on the loop? 18. Explain the principle and working of a cyclotron with the help of a labeled diagram. A cyclotron's oscillator frequency is 10Mhz. What should be the operating magnetic field for accelerating protons? If the radius of its 'dees' is 60 cm, what is the kinetic energy of the proton beam produced by the accelerator? Express your answer in units of Me V. 19. Two wires of equal lengths are bent in the form of two loops. One of the loops is square shaped whereas the other loop is circular. These are suspended in a uniform magnetic field and the same current is passed through them. Which loop will experience greater torque? Give reasons. 20. An electron and a proton, moving parallel to each other in the same direction with equal momenta, enter into a uniform magnetic field which is at right angles to their velocities. Trace their trajectories in the magnetic field. 21. A charged particle enters into a uniform magnetic field and experiences upward force as indicated in the figure. What is the charge sign on the particle?

12 22. (a) State Biot Savart's law. Using this law, derive the expression for the magnetic field due to a current carrying circular loop of radius 'R', at a point which is at a distance 'x' from its centre along the axis of the loop. (b) Two small identical circular loops, marked (1) and (2), carrying equal currents, are placed with the geometrical axes perpendicular of each other as shown in the figure. Find the magnitude and direction of the net magnetic field produced at the point O. 23. (a) With the help of a labelled diagram, explain the principle and working of a moving coil galvanometer. (b) Two parallel coaxial circular coils of equal radius 'R' and equal number of turns 'N', carry equal currents 'I' in the same direction and are separated by a distance '2R'. Find the magnitude and direction of the net magnetic field produced at the midpoint of the line joining their centers. 24. Galvanometer with a coil of resistance 120Ω shows full scale deflection for a current of 2.5 ma. How will you convert the galvanometer into an ammeter of range 0 to 7.5 A? Determine the net resistance of the ammeter. When an ammeter is put in a circuit, does it read slightly less or more than the actual current in the original circuit? Justify your answer. 25. An electron beam projected along +X axis, experiences a force due to a magnetic field along the +ve Y axis. What is the direction of the magnetic field? 26. A coil of number of turns N, area A, is rotated at constant angular speed, in a uniform magnetic field B, and connected to a resistor R. Deduce expression for: (i) Maximum emf induced in the coil (ii) Power dissipation in the coil. 27. Two long parallel straight wires X and Y separated by a distance of 5 cm in air carry currents of 10A and 5A respectively in opposite directions. Calculate the magnitude and direction of the force on a 20 cm length of the wire Y. 28. A circular coil of100 turns, radius 10 cm carries a current of 5 A. it is suspended vertically in a uniform horizontal magnetic field of 0.5 T, the field lines making an angle of 60 0 with the of the plane of the coil. Calculate of the torque must be applied on it to prevent it from turning. 29. A hydrogen ion of mass m and charge q travels with a speed v in a circle of radius r in a magnetic field of intensity B. Write the equation in terms of these quantifies only, relating the force on the ion to the required centripetal force. Hence derive an expression for its time period. 30. A circular coil of 200 turns, radius 5cm carries a current of 2.5 A. It is suspended vertically in a uniform horizontal magnetic field of 0.25 T, with the plane of the coil making an angle of 60 0 with the field lines. Calculate the magnitude of the torque that must be applied on it to prevent it from turning. 31. What is the direction of the force acting on a charged particle q, moving with a velocity in a uniform magnetic field? 32. Why should the spring / suspension wire in a moving coil galvanometer have low torsional constant? 33. A circular coil of 200 turns and radius 10 cm is placed in a uniform magnetic field of 0.5 T, normal to the plane of the coil. If the current in the coil is 30A, calculate the: (a) total torque on the coil. (b) Total force on the coil. (c) Average force.

13 34. Using Ampere s circuital law, derive an expression for the magnetic field along the axis of a current carrying toroidal solenoid of N number of turns having radius r. 35. A particle of mass m, with charge q moving with a uniform speed v, normal to a uniform magnetic field B describes a circular path of radius r. Derive expressions for the (i) time period of revolution and (ii) kinetic energy of the particle. 36. Using Ampere s circuital law, derive an expression for the magnetic field along the axis of a toroidal solenoid. 37. Two long parallel straight wires X and Y separated by a distance of 2.5 cm in air carry currents of 5A and 2.5A respectively in opposite directions. Calculate the magnitude and direction of the force on a 10cm length of the wire Y. 38. Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid. Why? 39. A current I flows in a conductor placed perpendicular to the plane of the paper. Indicate the direction of the magnetic field due to a small element at point P situated at a distance from the element as shown in the figure. 40. A charge q moving along the X axis with a velocity is subjected to a uniform magnetic field B acting along the axis as it crosses the origin O. (i) Trace its trajectory. (ii) Does the charge gain kinetic energy as it enters the magnetic field? Justify your answer. 41. Write the expression for the magnetic moment. 42. A long straight wire of a circular cross section of radius a carries a steady current I. The current is uniformly distributed across the cross section. Apply Ampere s circuital law to calculate the magnetic field at a point r in the region for (i) r < a (ii) r > a. 43. Write two reasons why a galvanometer can not be used as such to measure current. 44. In the given figure this loop is placed in a horizontal plane near a long straight conductor carrying a steady current I 1 at a distance l as shown. Give reasons to explain that the loop will experience a net force, but no torque. Write the expression for this force acting on the loop. 45. A long straight wire AB carries I. A proton P travels with a speed v, parallel to the wire at a distance d from it in a direction opposite to the current as shown in the figure. What is the force experienced by the proton and what is its direction? 46. (a) With the help of a diagram, explain the principle and working of a moving coil galvanometer. (b) What is the importance of a radial magnetic field and how is it produced? (c) Why is it that using a moving coil galvanometer as a voltmeter a high resistance in series is required whereas in an ammeter a shunt is used? 47. A rectangular loop and a circular are moving out of a uniformly magnetic field to a field free region with constant velocity v as shown in the figure. Explain in which loop do you expect the induced emf to be constant during the passage out of the field region. The magnetic field is normal to the loops. 48. An particle and a proton are accelerated from rest by the same potential. Find the ratio of their de-broglie wavelengths.

14 49. Deduce the expression for the magnetic dipole moment of an electron orbiting around the central nucleus. 50. A circular coil of N turns and radius R carries a current I. It is unwound and rewound to make another coil of radius R/2, current I remaining the same. Calculate the ratio of the magnetic moments of the new coil and the original coil. 51. (a) Explain giving reasons, the basic difference in converting a galvanometer into (i) a voltmeter and (ii) an ammeter? 52. A circular coil of N turns and diameter d carries a current I. It is unwound and rewound to make another coil of diameter 2d, current I remaining the same. Calculate the ratio of the magnetic moments of the new coil and the original coil. 53. A circular coil of closely wound N turns and radius r carries a current I. Write the expressions for following: (i) the magnetic field at its centre. (ii) the magnetic moment of this coil. 54. A rectangular loop of wire of size 4 cm 10 cm carries a steady current of 2A. A straight long wire carrying 5A current is kept near the loop as shown. If the loop and the wire are coplanar, find (i) the torque acting on the loop and (ii) the magnitude and direction of the force on the loop due to the current carrying wire. 55. Two identical circular loops, P and Q, each of radius r and carrying equal currents are kept in the parallel planes having a common axis passing through O. The direction of current in P is clockwise and in Q is anticlockwise as seen from O which is equidistant from the loops P and Q. Find the magnitude of the net magnetic field at O. 56. A rectangular loop of wire of size 2.5 cm 4 cm carries a steady current of 1 A. A straight wire carrying 2 A current is kept near the loop as shown. If the loop and the wire are coplanar, find the (i) torque acting on the loop and (ii) the magnitude and direction of the force on the loop due to the current carrying wire. 57. Two identical circular wires P and Q each of radius R and carrying current 'I' are kept in perpendicular planes such that they have a common centre as shown in the figure. Find the magnitude and direction of the net magnetic field at the common centre of the two coils. 58. A straight conducting rod of length.06m and mass 30g is suspended by two vertical wires at its ends. A current of 1 A is set up in the rod. Find (a) what magnetic field should be set up normal to the conductor so that tension in the wire is zero? (b) what will be the total tension in the wire if the direction of the current is reversed. 59. A very long wire carrying a current I =10 A is bent at right angles. Find the magnetic induction at a point lying on a perpendicular to the wires drawn through the point of bending, at a distance l= 30 cm from it. 60. In an ammeter, 0.5% of main current pass through galvanometer. If resistance of galvanometer is G, what will be the resistance of ammeter? 61. The plane of a rectangular loop of wire of sides 0.05m and 0.08m is placed in a uniform magnetic field of induction 1.5 x 10 2 T. A current of 10.0 amp flows through the loop. The plane of the coils is normal to the lines of induction. What is the torque acting on it? 62. Derive the formula for magnetic field on the axis of a circular current loop? 63. Differentiate between a solenoid and a toroid.

15 64. Define Lorentz force? What is cyclotron frequency? 65. A galvanometer has a resistance of 55 ohms. It gives full scale deflection by a current of 10mA. What resistance must be connected across it to enable it to read 1 ampere? 66. What is the force on a charged particles when it is moving at right angle to the applied magnetic field? 67. Why a galvanometer cannot be used as an ammeter directly? 68. What is the magnitude of magnetic field at a distance R from a long straight wire carrying a current I? 69. What is the resistance of an ideal ammeter? 70. When will be the force experienced by a moving charge in a magnetic field maximum? 71. What happens to the speed and kinetic energy of a particle when it is projected perpendicular to the magnetic field? 72. How ammeter and voltmeter is connected in a circuit? 73. Which will experience greater torque? A circular loop or a square loop having same current and placed in a uniform magnetic field. 74. An particle of mass 6.65 x10 27 kg is traveling at right angles to a magnetic field with a speed of 6 x10 5 m/s. The strength of the magnetic field is 0.2T. Determine the force on the particle and its acceleration. 75. A long straight conductor carries a current of 100 A. At what distance from the conductor is the magnetic field caused by the current equivalent to 0.5 x10 4 T? 76. Find an expression for magnetic field induction at the centre of a coil curved in the form of a square of side 2a, carrying current I. 77. An electric current is flowing in a circular coil of radius a. At what distance from the centre on the axis of the coil will be magnetic field be 1/8th of its value at the centre? 78. A current of 5 A is flowing from south to north inside a straight wire. Find the magnetic field due to a 1 cm piece of wire at a point 1 m northeast from the piece of wire. 79. A proton moving in a straight line enter a strong magnetic field alongside the field direction. How will its path and velocity gets affected? 80. Does a magnetic field exert a force on a static charge? 81. The net charge in a current carrying conductor is zero, even then it experiences a force in a magnetic field. Why? 82. The equation F = qvbsin involves the magnitude of three vectors which pair of vectors is always at right angles? 83. If an electron is not deflected in passing through a certain region of space, can we be sure that there is no magnetic field in this region? 84. A charged particle moves right angles to a magnetic field. How its kinetic energy and momentum gets affected? 85. No work is done when a charged particle moves right angle to the magnetic field. Why? 86. Free electrons always keep on moving in a conductor. Even then, no magnetic force act on them in a magnetic field except a current is passed through it. Why?

16 87. There is a thin conducting wire carrying current. What should be the value of magnetic field induction at any point on the conductor itself? 88. Explain the rule with illustration, related to the direction of current through a conductor and magnetic field. 89. A solenoid of length 0.5 m has a radius of 1 cm and is prepared up of 500 turns. It carries a current of 5A. What is the magnitude of the magnetic field within the solenoid? 90. Where is the magnetic field due to current through a circular loop uniform? 91. A closely wound smooth circular coil of 25 turns of wire has diameter 0.10 m and carry a current of 4 ampere. Establish the flux density at the centre of a coil. 92. A solenoid of length 1m has 5 layers of 1400 turns each one but the current through the solenoid is 2A, compute the flux density at the centre. 93. A solenoid of length 0.25 m through an iron core, is wound with 100 turns of wire and a current of 2A if passed through it. If the magnetic flux density formed at the centre of the core is 2.5 T, compute the relative permittivity of the core. 94. Find the magnetic induction at centre O due to current i through the circuit shown in the figure below. 95. A wire loop carry a current I as shown. Find an expression for the magnetic field formed at the centre O. 96. What types of deformation do you expect in a solenoid when a very strong impulse of current is passed through a broad winding of a solenoid? 97. A length of wire carries a steady current. It is curved, first, to form a circular plane coil of one turn. The similar length is, now bent more sharply to give a double loop of smaller radius. How does the magnetic induction at the centre alter? 98. The magnetic field at a tip near the centre but outside a current carrying solenoid is zero. Explain Why? 99. A current is flowing in circular coil of radius r and the magnetic field at its centre is B 0. At what distance from the centre on the axis of the coil, the magnetic field determination be B 0 /8? 100. If a long level conductor is bent as shown and a current I is accepted in it. Determine the magnitude and direction of magnetic field induction at the centre of circular part A solenoid 50 cm long has 4 layers of windings of 350 turns each. The radius of the lowest layer is 1.4 cm. If the current carried is 6.0 A, estimate the magnitude of magnetic flux density Two parallel coaxial circular coils of equal radius R and equal number of turns N carry equal currents I in the same direction and are separated by a distance 2 R. Locate the magnitude and direction of the remaining magnetic field formed at the midpoint of the line joining their centers The wires which connect the battery of a car to its starting motor carries a current of 300 A. What is the force per unit length between the wires if they are 70 cm long and 1.5 cm apart? What is the nature of the force? 104. Why two straight parallel metallic wires carrying current in the opposite directions repel each other? 105. Why is ammeter connected in series and voltmeter in parallel to the circuit?

17 106. Two long parallel straight wires A and B separated by a distance of 5 cm in air carry currents of 10A and 5 A, respectively in opposite directions. Calculate the magnitude and direction of the force on a 20 cm length of the wire B A circular coil of 20 turns and radius 10 cm carries a current of 5 A. It is placed in a uniform magnetic field of T. Find the torque acting on the coil when the magnetic field is applied (a) normal to the plane of the coil (b) in the plane of coil. Also find out the total force acting on the coil A rectangular coil of area 5.0 x10 4 m 2 and 60 turns is pivoted about one of its vertical sides. The coil is in a radial horizontal field of 90 G (radial here means the field lines are in the plane of the coil for any rotation). What is the torsional constant of the hair springs connected to the coil, if a current of 2 ma produces an angular deflection of A circular coil of 100 turns, radius 10 cm carries a current of 5 A. It is now suspended vertically in a uniform horizontal magnetic field of 0.5 T, the field lines making an angle of 60 0 with the plane of coil. Evaluate the magnitude of the torque that must be applied on it to avert it from turning A current carrying loop, free to turn, is located in a uniform magnetic field. What will be its orientation, relation to B, in the equilibrium position? 111. Why do we not use galvanometer as an ammeter?

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