Title 20. Moving Charges and Magnetism Hard.pdf ✅

1. A wire in the form of a square of side a carries a current i. Then the magnetic induction at the centre of the square wire is (Magnetic permeability of free space = 0) (a) 2 a i 0   (b) a i 2 0   (c) a 2 2 i 0   (d) 2 a i0   2. The ratio of the magnetic field at the centre of a current carrying circular wire and the magnetic field at the centre of a square coil made from the same length of wire will be (a) 4 2 2  (b) 8 2 2  (c) 2 2  (d) 4 2  3. The field B at the centre of a circular coil of radius r is  times that due to a long straight wire at a distance r from it, for equal currents here shows three cases; in all cases the circular part has radius r and straight ones are infinitely long. For same current the field B is the centre P in cases 1, 2, 3 has the ratio (a)       −                − 2 1 4 3 : 2 : 2 (b)       +        +        +  − 2 1 4 3 1 : 2 1 : 2 (c) 4 3 : 2 : 2    − (d)       +        −        −  − 2 1 4 3 : 2 1 2 1 : 2 4. Two infinite length wires carries currents 8A and 6A respectively and placed along X and Y-axis. Magnetic field at a point P (0, 0, d)m will be (a) d 7 0   (b) d 10 0   (c) d 14 0   (d) d 5 0   5. An equilateral triangle of side 'a' carries a current i then find out the magnetic field at point P which is vertex of triangle (a) 2 3 a i 0    (b) 2 3 a i 0    (c) a 2 3 i 0    (d) Zero 6. The earth’s magnetic induction at a certain point is 5 2 7 10 Wb / m −  . This is to be annulled by the magnetic induction at the centre of a circular conducting loop of radius 5 cm. The required current in the loop is (a) .56 A (b) 5.6 A (c) 0.28 A (d) 2.8 A 7. A particle carrying a charge equal to 100 times the charge on an electron is rotating per second in a circular path of radius 0.8 metre. The value of the magnetic field produced at the centre will be (0 − permeability for vacuum) (a) 0 7 10  − (b) 0 17 10  − (c) 0 6 10  − (d) 0 7 10  − 8. Ratio of magnetic field at the centre of a current carrying coil of radius R and at a distance of 3R on its axis is (a) 10 10 (b) 20 10 (c) 2 10 (d) 10 9. A circular current carrying coil has a radius R. The distance from the centre of the coil on the axis where the magnetic induction will be th 8 1 to its value at the centre of the coil, is (a) 3 R (b) R 3 (c) 2 3R (d) R 3 2 10. An infinitely long conductor PQR is bent to form a right angle as shown. A current I flows through PQR. The magnetic field due to this current at the point M is . H1 Now, another infinitely long straight conductor QS is connected at Q so that the current is 2 1 in QR as well as in QS, the current in PQ remaining unchanged. The magnetic field at M is now . H2 The ratio 1 2 H / H is given by (a) 2 1 (b) 1 (c) 3 2 (d) 2 11. Figure shows a square loop ABCD with edge length a. The resistance of the wire ABC is r and that of ADC is 2r. The value of magnetic field at the centre of the loop assuming uniform wire is (a) a i   3 2 0  (b)    3 a 2 i 0 (c) a 2 i 0    (d)    a 2 i 0 M P i +  S R –  90o 90o Q P i a i r i O r O i O 90o r i O i a
12. A long solenoid has 200 turns per cm and carries a current of 2.5 A. The magnetic field at its centre is [0 = 4 10–7Wb/m2 ] (a) 3.14  10–2Wb/m2 (b) 6.28  10–2Wb/m2 (c) 9.42  10–2Wb/m2 (d) 12.56  10–2Wb/m2 13. A long solenoid is formed by winding 20 turns/cm. The current necessary to produce a magnetic field of 20 millitesla inside the solenoid will be approximately         = − 10 Tesla - metre / ampere 4 0 7   (a) 8.0 A (b) 4.0 A (c) 2.0 AC (d) 1.0 A 14. Two solenoids having lengths L and 2L and the number of loops N and 4N, both have the same current, then the ratio of the magnetic field will be (a) 1: 2 (b) 2 :1 (c) 1: 4 (d) 4 :1 15. The average radius of a toroid made on a ring of non-magnetic material is 0.1 m and it has 500 turns. If it carries 0.5 ampere current, then the magnetic field produced along its circular axis inside the toroid will be (a) 2 25 10−  Tesla (b) 2 5 10−  Tesla (c) 4 25 10−  Tesla (d) 4 5 10−  Tesla 16. For the solenoid shown in figure. The magnetic field at point P is (a) ( 3 1) 4 ni 0 +  (b) 4 3 ni 0 (c) ( 3 1) 2 ni 0 +  (d) ( 3 1) 4 ni 0 −  17. Figure shows the cress sectional view of the hollow cylindrical conductor with inner radius 'R' and outer radius '2R', cylinder carrying uniformly distributed current along it's axis. The magnetic induction at point 'P' at a distance 2 3R from the axis of the cylinder will be (a) Zero (b) 72 R 5 i 0   (c) 18 R 7 i 0   (d) 36 R 5 i 0   18. Electrons move at right angles to a magnetic field of 2 1.5 10 −  Tesla with a speed of 6 10 / . 27  m s If the specific charge of the electron is 11 1.7 10 Coul/kg. The radius of the circular path will be (a) 2.9 cm (b) 3.9 cm (c) 2.35 cm (d) 3 cm 19. An electron (mass 9 10 . 31 kg − =  charge 1.6 10 . 19 coul − =  ) whose kinetic energy is 7.2 10 joule −18  is moving in a circular orbit in a magnetic field of 9 10 weber / m . −5 2  The radius of the orbit is (a) 1.25 cm (b) 2.5 cm (c) 12.5 cm (d) 25.0 cm 20. An electron and a proton enter a magnetic field perpendicularly. Both have same kinetic energy. Which of the following is true (a) Trajectory of electron is less curved (b) Trajectory of proton is less curved (c) Both trajectories are equally curved (d) Both move on straight line path 21. A proton and an  − particles enters in a uniform magnetic field with same velocity, then ratio of the radii of path describe by them (a) 1:1 (b) 1: 2 (c) 2 :1 (d) None of these 22. A proton and an  − particle enter a uniform magnetic field perpendicularly with the same speed. If proton takes 25  sec to make 5 revolutions, then the periodic time for the  − particle would be (a) 50 sec (b) 25 sec (c) 10 sec (d) 5 sec 23. A particle with 10–11 coulomb of charge and 10–7 kg mass is moving with a velocity of 108 m/s along the y-axis. A uniform static magnetic field B = 0.5 Tesla is acting along the x- direction. The force on the particle is (a) 5  10–11 N along i ˆ (b) 5  103 N along k ˆ (c) 5  10–11 N along j ˆ − (d) 5  10–4 N along k ˆ − 24. An electron is moving along positive x-axis. To get it moving on an anticlockwise circular path in x-y plane, a magnetic filed is applied (a) Along positive y-axis (b) Along positive z-axis (c) Along negative y-axis (d) Along negative z-axis 25. A particle of charge 18 16 10 − −  coulomb moving with velocity 10 m/s 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 104 V/m is along the negative z-axis. If the charged particle continuous moving along the x-axis, the magnitude of B is (a) 3 2 10 Wb / m − (b) 3 2 10 Wb / m (c) 5 2 10 Wb / m (d) 16 2 10 Wb / m 26. A particle of mass m and charge q moves with a constant velocity v along the positive x direction. It enters a region containing a uniform magnetic field B directed along the negative z direction extending from x = a to x = b. The minimum value of v required so that the particle can just enter the region x > b is (a) qbB/m (b) q(b – a)B/m (c) qaB/m (d) q(b+a)B/2m 27. At a certain place magnetic field vertically downwards. An electron approaches horizontally towards you and enters in this 2R R 3R/2 n turn 30o 60o P
magnetic fields. It's trajectory, when seen from above will be a circle which is (a) Vertical clockwise (b) Vertical anticlockwise (c) Horizontal clockwise (d) Horizontal anticlockwise 28. When a charged particle circulates in a normal magnetic field, then the area of it's circulation is proportional to (a) It's kinetic energy (b) It's momentum (c) It's charge (d) Magnetic fields intensity 29. An electron moves straight inside a charged parallel plate capacitor at uniform charge density  . The space between the plates is filled with constant magnetic field of induction B. Time of straight line motion of the electron in the capacitor is (a) lB e 0   (b)   0 lB (c) B e 0   (d)   e 0B 30. A proton of mass 27 1.67 10 −  kg and charge 19 1.6 10 −  C is projected with a speed of 2 10 m / s 6  at an angle of 600 to the X-axis. If a uniform magnetic field of 0.104 Tesla is applied along Y-axis, the path of proton is (a) A circle of radius = 0.2 m and time period 7 10 −   s (b) A circle of radius = 0.1 m and time period 7 2 10 −   s (c) A helix of radius = 0.1 m and time period 7 2 10 −   s (d) A helix of radius = 0.2 m and time period 7 4 10 −   s 31. A charge particle, having charge q accelerated through a potential difference V enter a perpendicular magnetic field in which it experiences a force F. If V is increased to 5V, the particle will experience a force (a) F (b) 5F (c) 5 F (d) 5F 32. The magnetic field is downward perpendicular to the plane of the paper and a few charged particles are projected in it. Which of the following is true (a) A represents proton and B and electron (b)Both A and B represent protons but velocity of A is more than that of B (c) Both A and B represents protons but velocity of B is more than that of A (d) Both A and B represent electrons, but velocity of B is more than that of A 33. Two very long straight, particle wires carry steady currents i and – i respectively. The distance between the wires is d. At a certain instant of time, a point charge q is at a point equidistant from the two wires, in the plane of the wires. It's instantaneous velocity v is perpendicular to this plane. The magnitude of the force due to the magnetic field acting on the charge at this instant is (a) 2 d 0 iqv   (b) d 0 iqv   (c) d 2 0 iqv   (d) Zero 34. Wires 1 and 2 carrying currents 1 t and 2 t respectively are inclined at an angle  to each other. What is the force on a small element dl of wire 2 at a distance of r from 1 (as shown in figure) due to the magnetic field of wire 1 (a)    i ,i dl tan 2 r 1 2 0 (b)    i ,i dlsin 2 r 1 2 0 (c)    i ,i dl cos 2 r 1 2 0 (d)    i ,i dlsin 4 r 1 2 0 35. A conductor PQRSTU, each side of length L, bent as shown in the figure, carries a current i and is placed in a uniform magnetic induction B directed parallel to the positive Y-axis. The force experience by the wire and its direction are (a) 2iBL directed along the negative Z-axis (b) 5iBL directed along the positive Z-axis (c) Ibl direction along the positive Z-axis (d) 2iBL directed along the positive Z-axis 36. A conductor in the form of a right angle ABC with AB = 3cm and BC = 4 cm carries a current of 10 A. There is a uniform magnetic field of 5T perpendicular to the plane of the conductor. The force on the conductor will be (a) 1.5 N (b) 2.0 N (c) 2.5 N (d) 3.5 N 37. A wire of length l carries a current i along the X-axis. A magnetic field exists which is given as B = B0 ( ) ˆ ˆ ˆ i + j + k T. Find the magnitude of the magnetic force acting on the wire (a) B il 0 (b) B0 i l 2 (c) 2B i l 0 (d) B i l 2 1  0 38. A conducting loop carrying a current i is placed in a uniform magnetic field pointing into the plane of the paper as shown. (a) The loop will have a tendency to (b) Contract (c) Expand (d) Move towards + ve x-axis 39. A circular loop of radius a, carrying a current i, is placed in a two-dimensional magnetic field. The centre of the loop coincides with the centre of the field. The strength of the Z R Q P Y T U B → i S X i1 i2 dl  r                                      A B                                    l e –
magnetic field at the periphery of the loop is B. Find the magnetic force on the wire (a) i a B (b) 4i a B (c) Zero (d) 2i a B 40. A wire abc is carrying current i. It is bent as shown in fig and is placed in a uniform magnetic field of magnetic induction B. Length ab = l and abc = 45o . The ratio of force on ab and on bc is (a) 2 1 (b) 2 (c) 1 (d) 3 2 41. Current i flows through a long conducting wire bent at right angle as shown in figure. The magnetic field at a point P on the right bisector of the angle XOY at a distance r from O is (a) r i 0   (b) r 2 i 0   (c) ( 2 1) 4 r i 0 +   (d) ( 2 1) r 2i . 4 0 +   42. A long wire A carries a current of 10 amp. Another long wire B, which is parallel to A and separated by 0.1 m from A, carries a current of 5 amp. in the opposite direction to that in A. What is the magnitude and nature of the force experienced per unit length of B [ 7 0 4 10 −  =   weber/amp – m] (a) Repulsive force of 10 N / m −4 (b) Attractive force of 10 N / m −4 (c) Repulsive force of 2 10 N / m −5   (d) Attractive force of 2 10 N / m −5   43. Three long, straight and parallel wires carrying currents are arranged as shown in figure. The force experienced by 10 cm length of wire Q is (a) .4×10–4 N towards the right (b) 1.4×10–4 N towards the left (c) 2.6 × 10–4 N to the right (d) 2.6×10–4 N to the left 44. What is the net force on the coil (a) N 7 25 10 −  moving towards wire (b) N 7 25 10 −  moving away from wire (c) N 7 35 10 −  moving towards wire (d) N 7 35 10 −  moving away from wire 45. A long wire AB is placed on a table. Another wire PQ of mass 1.0 g and length 50 cm is set to slide on two rails PS and QR. A current of 50A is passed through the wires. At what distance above AB, will the wire PQ be in equilibrium (a) 25 mm (b) 50 mm (c) 75 mm (d) 100 mm 46. An infinitely long, straight conductor AB is fixed and a current is passed through it. Another movable straight wire CD of finite length and carrying current is held perpendicular to it and released. Neglect weight of the wire (a) The rod CD will move upwards parallel to itself (b) The rod CD will move downward parallel to itself (c) The rod CD will move upward and turn clockwise at the same time (d) The rod CD will move upward and turn anti –clockwise at the same time 47. A circular coil of radius 4 cm and 20 turns carries a current of 3 ampere. It is placed in a magnetic field of 0.5 T. The magnetic dipole moment of the coil is (a) 0.60 A-m2 (b) 0.45 A-m2 (c) 0.3 A-m2 (d) 0.15 A-m2 48. A steady current i flows in a small square loop of wire of side L in a horizontal plane. The loop is now folded about its middle such that half of it lies in a vertical plane. Let 1 and  2 respectively denote the magnetic moments due to the current loop before and after folding. Then (a) 2 = 0 (b) 1 and 2 are in the same direction (c) 2 | | | | 2 1 =   (d)         =   2 1 | | | | 2 1 49. A circular loop of area 1 cm2 , carrying a current of 10 A, is placed in a magnetic field of 0.1 T perpendicular to the plane of the loop. The torque on the loop due to the magnetic field is A B i1 C D i2 A 50 A B P Q S R 2A 2 cm 10 cm 15 cm 1A 45o P X Y r i O l B → 45o a c i i b i Y a B