Tiêu đề 1. ELECTROMAGNETISM & EMI_Final (PART-I) (01-38).pdf ✅

IIT ADVANCED NAME OF THE TOPIC NISHITH Multimedia India (Pvt.) Ltd., 1 JEE MAINS - CW - VOL - I ELECTROMAGNETISM & EMI NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL-VII ELECTROMAGNETISM & EMI LEVEL- V SINGLE ANSWER QUESTIONS MAGNETIC FIELD DUE TO CURRENT CARRYING CONDUCTOR 1. Two parallel, long wires carry currents i1 and i 2 with i1 > i2 . When the currents are in the same direction, the magnetic field at a point midway between the wires is 30 T . If the direction of 1 i is reversed, the field becomes 90 T . The ratio 1 2 i / i is (A) 4 (B) 3 (C) 2 (D) 1 2. In the given figure the magnitude of magnetic field at O is (all three wires are quarter circular arcs) Y Z X R R R O (A) 0 3 4 l R  (B) 0 3 2 l R  (C) 0 3 8 l R  (D) 0 3 6 l R  3. Two infinitely long, thin, insulated, straight wires lie in the x - y plane along the x and y- axes respectively. Each wire carries a current i, respectively in the positive x-direction and positive y-direction. The magnetic field will be zero at all points on the straight line (A) y = x (B) y=– x (C) y=x–1 (D)y=–x+1 4. B along the axis of a long solenoid is given by (A) B (B) B (C) B (D) B MOTION OF CHARGE PARTICLE IN MAGNETIC FIELD 5. An ionized gas contains both positive and negative ions. If it is subjected simultaneously to an electric field along the +x direction and a magnetic field along the +z direction, then (A) positive ions deflect towards +y direction and negative ions towards –y direction (B) all ions deflect towards +y direction (C) all ions deflect towards –y direction (D) positive ions deflect towards –y direction and negative ions towards +y direction. 6. A charged particle is released from rest in a region of steady and uniform electric and magnetic fields which are parallel to each other. The particle will move in a (A) straight line (B) circle (C) helix (D) cycloid. 7. A charged particle of mass m and charge q enters a magnetic field B with a velocity v at an angle θ with the direction of B. The radius of the resulting path is (A) B sin θ q mv (B) qBsin θ mv (C) qB mv (D) B tanθ q mv 8. A particle of mass m and charge q is projected into a region having a perpendicular uniform magnetic field B. Find the angle of deviation  of the particle as it comes out of the magnetic field if width d of the region is 2 m qB  (a) 0 30 (b) 0 60 (c) 0 45 (d) 0 90
2 NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL-VII NISHITH Multimedia India (Pvt.) Ltd., ELECTROMAGNETISM & EMI 9. Length of two parallel conducting plates is 0.17 m and separation between them is 0.1 m. A uniform electric field of 3 10 /  E N C  is present in the space between the plates. A charged particle having charge 6 10 C and mass 10 10 Kg is fired from middle of the plates at an angle 0 30 with plane of plates as shown in the figure there exist a uniform magnitic field perpendicular to the plane of figure in the space outside the plates what should be the magnitude of the magnitic field so that the particle grazes the plates at P and Q (neglect the gravity) (a) 3.4 mT (b) 4.3 mT (c) 2.3 mT (d) 5.3 mT FORCE ACTING ON A CURRENT CARRYING CONDUCTOR 10. Two thin long parallel wires separated by a distance b carry currents of equal magnitude i . The magnitude of the force per unit length exerted by one wire on the other is (A) 2 2 0 b μ i (B) 2πb μ 2 0 i (C) 2πb μ0 i (D) 2 0 πb μ i 11. A conducting loop carrying a clockwise current ‘i’ is placed in a uniform magnetic field pointing into the plane of the paper as shown. the loop will have a tendency to (A) contract (B) expand (C) move towards positive x - axis (D) move towards negative x - axis 12. Two long conducting rods suspended by means of two insulating threads as shown in figure, are connected to a charged capacitor through a switch which is initially open. At the other end, they are connected by a loose wire. The capacitor has a charge Q and mass per unit length of the rod is . The effective resistance of the circuit after closing the switch is R. What is the velocity of each rod when the capacitor is discharged after closing the switch. Assume that the displacement of rods during the discharging time is negligible. (A) 2 0 4 Q dRC   (B) 0 4 Q dRC   (C) 3 0 4 Q dRC   (D) 4 0 4 Q dRC   13. A rod of mass m and radius R rests on two parallel rails that are a distance l apart and have a length L. The rod carries a current I (in the direction shown) and rolls along the rails without slipping. A uniform magnetic field B is directed perpendicular to the rod and the rails. If it starts from rest, what is the speed of the rod as it leaves the rails? (a) 4 3 BIlL m (b) 3 3 BIlL m (c) 4 2 BIlL m (d) BIlL m
IIT ADVANCED NAME OF THE TOPIC NISHITH Multimedia India (Pvt.) Ltd., 3 JEE MAINS - CW - VOL - I ELECTROMAGNETISM & EMI NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL-VII 14. A straight piece of conducting wire with mass M and length L is placed on a frictionless incline tilted at an angle  from the horizontal (as shown in figure). There is a uniform, vertical magnetic field at all points (produced by an arrangement of magnets not shown in fiugure) : To prevent the wire from sliding down the incline, a voltage source is attached to the ends of the wire. When just the right amount of current flows through the wire, the wire remains at rest. Detrmine the magnitude and direction of the current in the wire that will cause the wire to remain at rest. (a) tan 2 Mg LB  to the left (b) Mgtan LB  to the right (c) Mg tan LB  to the left (d) 3 tan 2 Mg LB  to the left MAGNETIC MOMENT OF A CURRENT CARRYING LOOP & IT PLACED IN AN EXTERNAL MAGNETIC FIELD 15. An insulating rod of length l carries a charge q distributed uniformly on it. The rod is pivoted at an end and is roated at a frequency f about a fixed perpendicular axis. The magnetic moment of the system is (A) zero (B) 2 qfl (C) 1 2 qf 2  l (D) 1 2 qf 3  l 16. A current carrying wire frame is in the shape of digit eight (8). It is carrying current i0 . If the radius of each loop is R0 , then the net magnetic dipole moment of the figure is: R0 x-axis y-axis i0 (A) 2 0 0 (i R ) 2  (B) zero (C) 2 0 0 i 2 R   (D) 0 0 i (4 R )   17. Two points A and B of non-uniform circular conductor are connected to two batteries as shown in figure-(a). Assuming the magnetic induction at C due to the current in the circular part only, calculate magnetic induction at C. The radius of loop equals 1 7 7 cm . Each of the two parts of the circular loop has a resistance equal to 2.5 . (a) 6 8.21 10 T   (b) 6 82.1 10 T   (c) 6 8.1 10 T   (d) 6 8 10 T   18. ‘Q’ charge is uniformly distributed over the surface of a right circular cone of semivertex angle  and height h. The cone is uniformly rotated about its axis at angular velocity . Calculate the associated magnetic dipole moment. (a)  2 2 tan 4 Q h n   (b)  2 2 tan 2 Q h n   (c)  2 2 tan 3 Q h n   (d) 2 2  Q h n   tan MAGNETIC FIELD DUE TO CURRENT CARRYING CONDUCTOR 19. The magnetic field at the centre O of the circular portion of radius 3 cm carrying current 4 ampere in the wire is O A E C 4amp  B D (A) 8 3 10 T 5 /  (B) 8 3 10 T 4 /  (C) 2 10 T 5  (D) 2 10 T 4 
4 NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL-VII NISHITH Multimedia India (Pvt.) Ltd., ELECTROMAGNETISM & EMI 20. An infinitely long conductor PQR is bent to form a right angle. 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 I/2 in QR as well as in QS, the current in PQ remaining unchanged. The magnetic field at M is now H2 . The ratio H1 /H2 is given by: (A) 1/2 (B) 1 (C) 2/3 (D)2 21. A sphere of radius R, uniformly charged with the surface charge density  , rotates around the axis passing through its centre at an angular velocity . The magnetic induction at the centre of the rotating sphere and its magnetic moment, respectively are (a)  0   2 3  R k , 4 4 3   R (b)    2 0 2 3  R k , 4 4 3   R (c)    3 0 2 3  R k , 4 4 3   R (d)    4 0 2 3  R k , 4 4 3   R 22. A conductor carries a constant current I along the closed path abcdefgha involving 8 of the 12 edges of length l . The magnetic dipole moment of the closed path is (a) 2  l I j (b) 3  l I j (c) 4  l I j (d) 5  l I j 23. A long current wire is bent in the shapes shown in figure. The circular portion has radius R. The magnetic induction at the center of the circular segment is (a) 0  2 4 I k i R          ,    0 1 4 I k i R           , 0   3 4 2 I k j i R              (b) 0  2 4 I k i R         ,    0 1 4 I k i R           , 0   3 4 2 I k j i R             (c) 0  2 4 I k i R          ,    0 1 4 I k i R          , 0   3 4 2 I k j i R             (d) 0  2 4 I k i R         ,    0 1 4 I k i R          , 0   3 4 2 I k j i R             MOTION OF CHARGE PARTICLE IN MAGNETIC FIELD 24. An electron with a speed u along the positive x–axis at y = 0 enters a region of uniform magnetic field B = – B0 k which exists in the region where y > 0. The electron exits from the region after some time with the speed v at co–ordinate y, then (A) v > u, y < 0 (B) v = u, y > 0 (C) v > u, y > 0 (D) v = u, y < 0 25. A particle moves in a circular path of diameter 1.0 m under the action of magnetic field of 0.40 Tesla. An electric field of 200 V/m makes the path of particle straight. Find the charge / mass ratio of the particle (A) 2.5 × 103C/kg (B) 5 2 10 /kg  C (C) 5 3.5 10 /kg  C (D) 5 3 10 /kg  C 26. A proton, a deutron and an α –particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If rP , rd and rα denote respectively the radii of the trajectories of these particles then (A) α p d r  r  r (B) α d p r  r  r (C) α d p r  r  r (D) p d α r  r  r