Title 20. Moving Charges and Magnetism Easy.pdf ✅

1. A length L of wire carries a steady current I. It is bent first to form a circular plane coil of one turn. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the centre caused by the same current is (a) A quarter of its first value (b) Unaltered (c) Four times of its first value (d) A half of its first value 2. A vertical straight conductor carries a current vertically upwards. A point P lies to the east of it at a small distance and another point Q lies to the west at the same distance. The magnetic field at P is (a) Greater than at Q (b) Same as at Q (c) Less than at Q (d) Greater or less than at Q depending upon the strength of the current 3. If a copper rod carries a direct current, the magnetic field associated with the current will be [CPMT 1984] (a) Only inside the rod (b) Only outside the rod (c) Both inside and outside the rod (d) Neither inside nor outside the rod 4. If a long hollow copper pipe carries a direct current, the magnetic field associated with the current will be (a) Only inside the pipe (b) Only outside the pipe (c) Neither inside nor outside the pipe (d) Both inside and outside the pipe 5. The magnetic field dB due to a small current element dl at a distance r and element carrying current i is, or Vector form of Biot-savart's law is (a)          = r dl r dB i   4 0 (b)          = r dl r dB i 0 2 4  (c)          = 2 r dl r dB i 0 2 4  (d)          = 3 r dl r dB i   4 0 6. A charge q coulomb moves in a circle at n revolutions per second and the radius of the circle is r metre. Then magnetic field at the centre of the circle is (a) 7 10 2 −  nr q N/amp/metre (b) 7 10 2 −  r q N/amp/metre (c) 7 10 2 −  r nq N/amp/metre (d) r 2q N/amp/metre 7. An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current of i ampere and the radius of the circular loop is r metre. Then the magnetic induction at its centre will be (a) ( 1) 2 4 0  +   r i (b) ( 1) 2 4 0  −   r i (c) Zero (d) Infinite 8. A current i ampere flows in a circular arc of wire whose radius is R, which subtend an angle 3 / 2 radian at its centre. The magnetic induction B at the centre is (a) R i 0 (b) R i 2 0 (c) R i 0 2 (d) R i 8 30 9. A current i ampere flows along the inner conductor of a coaxial cable and returns along the outer conductor of the cable, then the magnetic induction at any point outside the conductor at a distance r metre from the axis is (a)  (b) Zero (c) r 2i 4 0   (d) r  i   2 4 0 10. A straight section PQ of a circuit lies along the X-axis from 2 a x = − to 2 a x = and carries a steady current i. The magnetic field due to the section PQ at a point X = + a will be (a) Proportional to a (b) Proportional to 2 a (c) Proportional to 1 / a (d) Zero 11. A helium nucleus makes a full rotation in a circle of radius 0.8 metre in two seconds. The value of the magnetic field B at the centre of the circle will be (a) 0 19 10  − (b) 0 19 10  − (c) 0 10 2 10  −  (d) 0 10 2 10  −  12. A solenoid of 1.5 metre length and 4.0 cm diameter posses 10 turn per cm. A current of 5 ampere is flowing through it. The magnetic induction at axis inside the solenoid is (a) Tesla 3 2 10 −   (b) Tesla 5 2 10 −   (c) Gauss 2 4 10 −   (d) Gauss 5 2 10 −   r O i O R i /2
13. The magnetic induction at a point P which is distant 4 cm from a long current carrying wire is Tesla 8 10 − . The field of induction at a distance 12 cm from the same current would be (a) Tesla 9 3.33 10 −  (b) Tesla 4 1.11 10 −  (c) Tesla 3 3 10 −  (d) Tesla 2 9 10 −  14. The strength of the magnetic field at a point r near a long straight current carrying wire is B. The field at a distance 2 r will be (a) 2 B (b) 4 B (c) 2B (d) 4B 15. Field at the centre of a circular coil of radius r, through which a current I flows is (a) Directly proportional to r (b) Inversely proportional to I (c) Directly proportional to I (d) Directly proportional to 2 I 16. A current of 0.1 A circulates around a coil of 100 turns and having a radius equal to 5 cm. The magnetic field set up at the centre of the coil is ( 4 10 / ) 7 0 =  weber ampere −metre −   (a) tesla 5 4 10 −   (b) tesla 5 8 10 −   (c) tesla 5 4 10 −  (d) tesla 5 2 10 −  17. The magnetic field B with in the solenoid having n turns per metre length and carrying a current of i ampere is given by (a) e ni 0 (b) ni 0 (c) ni 0 4 (d) ni 18. The magnetic induction at the centre O in the figure shown is (a)         − 1 2 0 1 1 4 R R  i (b)         + 1 2 0 1 1 4 R R  i (c) ( ) 4 1 2 0 R R i −  (d) ( ) 4 1 2 0 R R i +  19. Field inside a solenoid is (a) Directly proportional to its length (b) Directly proportional to current (c) Inversely proportional to total number of turns (d) Inversely proportional to current 20. In the figure, shown the magnetic induction at the centre of there arc due to the current in portion AB will be (a) r i 0 (b) r i 2 0 (c) r i 4 0 (d) Zero 21. In the above question, the magnetic induction at O due to the whole length of the conductor is (a) r i 0 (b) r i 2 0 (c) r i 4 0 (d) Zero 22. In the figure shown there are two semicircles of radii 1 r and 2 r in which a current i is flowing. The magnetic induction at the centre O will be (a) ( ) 1 2 0 r r r i +  (b) ( ) 4 1 2 0 r r i −  (c)         + 1 2 0 1 2 4 rr  i r r (d)         − 1 2 0 2 1 4 rr  i r r 23. The magnetic moment of a current carrying loop is 25 2 2.110 amp m − . The magnetic field at a point on its axis at a distance of 1 Å is (a) 2 2 4.2 10 weber / m −  (b) 3 2 4.2 10 weber / m −  (c) 4 2 4.2 10 weber / m −  (d) 5 2 4.2 10 weber / m −  24. Two straight horizontal parallel wires are carrying the same current in the same direction, d is the distance between the wires. You are provided with a small freely suspended magnetic needle. At which of the following positions will the orientation of the needle be independent of the magnitude of the current in the wires (a) At a distance d / 2 from any of the wires (b) At a distance d / 2 from any of the wires in the horizontal plane (c) Anywhere on the circumference of a vertical circle of radius d and centre halfway between the wires (d) At points halfway between the wires in the horizontal plane R1 O R2 A B O C D r r1 O r2

38. The direction of magnetic lines of forces close to a straight conductor carrying current will be (a) Along the length of the conductor (b) Radially outward (c) Circular in a plane perpendicular to the conductor (d) Helical 39. If the strength of the magnetic field produced 10cm away from a infinitely long straight conductor is 5 2 10 Weber / m − , the value of the current flowing in the conductor will be (a) 5 ampere (b) 10 ampere (c) 500 ampere (d) 1000 ampere 40. Due to 10 ampere of current flowing in a circular coil of 10 cm radius, the magnetic field produced at its centre is 3 2 3.14 10 Weber / m −  . The number of turns in the coil will be (a) 5000 (b) 100 (c) 50 (d) 25 41. There are 50 turns of a wire in every cm length of a long solenoid. If 4 ampere current is flowing in the solenoid, the approximate value of magnetic field along its axis at an internal point and at one end will be respectively (a) 3 2 3 2 12.6 10 Weber / m , 6.3 10 Weber / m − −   (b) 3 2 3 2 12.6 10 Weber / m , 25.1 10 Weber / m − −   (c) 3 2 3 2 25.1 10 Weber / m , 12.6 10 Weber / m − −   (d) 5 2 5 2 25.1 10 Weber / m , 12.6 10 Weber / m − −   42. A solenoid is 1.0 metre long and it has 4250 turns. If a current of 5.0 ampere is flowing through it, what is the magnetic field at its centre [ 4 10 / ] 7 0 =  weber amp −m −   (a) 2 2 5.4 10 weber / m −  (b) 2 2 2.7 10 weber / m −  (c) 2 2 1.35 10 weber / m −  (d) 2 2 0.675 10 weber / m −  43. A vertical wire kept in Z-X plane carries a current from Q to P (see figure). The magnetic field due to current will have the direction at the origin O along (a) OX (b) OX' (c) OY (d) OY ' 44. One metre length of wire carries a constant current. The wire is bent to form a circular loop. The magnetic field at the centre of this loop is B. The same is now bent to form a circular loop of smaller radius to have four turns in the loop. The magnetic field at the centre of this new loop is (a) 4 B (b) 16 B (c) B / 2 (d) B / 4 45. In a hydrogen atom, an electron moves in a circular orbit of radius m 11 5.2 10 −  and produces a magnetic induction of 12.56 T at its nucleus. The current produced by the motion of the electron will be (Given 4 10 / ) 7 0 =  Wb A −m −   (a) ampere 3 6.53 10 −  (b) ampere 10 13.25 10 −  (c) ampere 6 9.6 10 (d) ampere 3 1.04 10 −  46. An arc of a circle of radius R subtends an angle 2  at the centre. It carries a current i. The magnetic field at the centre will be (a) R i 2 0 (b) R i 8 0 (c) R i 4  0 (d) R i 5 20 47. At a distance of 10 cm from a long straight wire carrying current, the magnetic field is 0.04 T. At the distance of 40 cm, the magnetic field will be (a) 0.01 T (b) 0.02 T (c) 0.08 T (d) 0.16 T 48. A uniform wire is bent in the form of a circle of radius R. A current I enters at A and leaves at C as shown in the figure :If the length ABC is half of the length ADC, the magnetic field at the centre O will be (a) Zero (b) R I 2 0 (c) R I 4 0 (d) R I 6 0 49. The magnetic induction at any point due to a long straight wire carrying a current is (a) Proportional to the distance from the wire (b) Inversely proportional to the distance from wire (c) Inversely proportional to the square of the distance from the wire (d) Does not depend on distance 50. The expression for magnetic induction inside a solenoid of length L carrying a current I and having N number of turns is (a) LI N   4 0 (b) NI 0 (c) NLI   4 0 (d) I L N  0 Y Z ' Q i X X Y Z P O A B C D O