1. Two identical co-axial circular loops carry equal currents circulating in the same direction: (a) The current in each coil decrease as the coils approach each other. (b) The current in each coil increase as the coils approach each other. (c) The current in each coil decrease as the coils move away from each other. (d) The current in each coil remains constant as the coils approach or move away from each other. 2. A uniform rod rotates in a uniform magnetic field B about end P with a constant angular velocity. Magnetic field B is parallel to. Length of the rod is l. Then: (a) a uniform electric field directed from P to Q is induced in the rod. (b) a uniform electric field directed from Q to P is induced in the rod. (c) a non-uniform electric field directed from Q to P is induced in the rod. (d) a non-uniform electric directed from P to Q is induced in the rod. 3. A straight rod of length l is rotating about an axis passing through O as shown. A uniform magnetic field B exists parallel to the axis of rotation. Emf induced between P and Q is: (a) 8 25 B l2 (b) 3 10 B l2 (c) 7 25 B l2 (d) zero 4. A vertical ring of radius r and resistance falls vertically. It is in contact with two vertical rails which are joined at the top. The rails are frictionless and has negligible resistance. Horizontal uniform magnetic field of magnitude B perpendicular to the plane of ring and rails exists. When the speed of ring is, the current in the section PQ is: (a) zero (b) 2Br 5. A circular loop is lying in X-Y plane with its centre at origin. A long straight wire passing through origin carries a current i in negative z-direction. The induced current in the coil is: (a) zero (b) clockwise (c) anti-clockwise (d) alternating 6. Figure shows a horizontal magnetic field which is uniform above the dotted line and is zero below it. A long, rectangular, conducting loop of wih L mass m, resistance is placed partly above and partly below the dotted line with the lower edge parallel to it. The velocity with which the loop be pushed downward so that it may continue to fall without any acceleration is: (a) mg B 2 l 2 mg (b) B 2 (c) 4 br (c) B2 l 2 mg (d) 8 Br (d) B2 l 2 mg 7. A 24 volt battery connected to a 12, 10 H coil through a switch drives a constant current in the circuit. The switch is suddenly opened. Assuming that it took 2 ms to open the switch, the average emf induced across the coil is: (a) 20000 V (b) 10000 volt (c) 2000 V (d) 1000 Volt 8. A conducting rod PQ of length 1 m is moving with uniform velocity of 2 m/s in a uniform magnetic field of 2T directed into the plane of paper. A capacitor of capacity c 10 F is connected as shown. Then (a) q A + 40 C, q B + 40 C (b) q A + 40 C, q B - 40 C (c) q A - 40 C, q B + 40 C (d) q A q B 0 9. A square wire loop side 2.0 m is perpendicular to a uniform magnetic field as shown. The loop contains a 2V battery of negligible resistance. If magnitude of magnetic field varies linearly with time according to B 0.05 0.5t with B in tesla and t in time, the total emf in the circuit is: (a) 0 (b) 2V (c) 1V (d) 4V 10. A metal disc of radius a and thickness d is placed in uniform magnetic field B B 0 sin t. The resistivity of metal is. Consider a ring a radius r and wih dr. The Eddy current developed in the ring is: (a) B 0 d cos t r dr (b) B 0 d sin t r dr (c) B 0 d sin t r dr (d) B 0 d cos t r dr 11. Magnetic flux changes from a coil of resistance 10. As a result an induced current is developed in it, which varies with time as shown. The magnitude of changes in flux through coil in webers is: (a) 2 (b) 2.5 (c) 4 (d) 6 12. A solenoid of inductance 50 mh and resistance 10 is connected to a battery of 6V. The time elapsed before the current acquires half of its steady value is (a) 2 ms (b) 3.5 ms (c) 5 ms (d) 5.5 ms
13. Two conducting rings of radii r and 2r move in opposite directions with velocities and respectively on a conducting surface S. There is a uniform magnetic field of magnitude B perpendicular to the plane of rings. The potential difference between the highest points of the two rings is: (a) zero (b) 2r B (c) 4r B (d) 8Br 14. Two straight conducting rails from a right angle where their ends are joined. A conducting bar in contact with the rails start at the vertex at t 0 and moves with a constant velocity along them as shown. A magnetic field B is directed into the page. The induced emf in the circuit at any time t is proportional to: (a) t 0 (b) t (c) (d) 2 15. A small square loop of wire of side l is placed inside a large square loop of wire of side L (>> l). The loops are coplanar and their centres coincide. The mutual inductance of the system is: (a) directly proportional to l 2 (b) inversely proportional to l 2 (c) directly proportional to L (d) inversely proportional to L 16. A conducting rod PQ of mass and length l moves on two frictionless parallel rails in the presence of uniform magnetic field directed into the page of paper. The rod is given an initial velocity 0 to the right and is released at t 0. At time t, velocity of rod is and induced current is i. Then: 17. The current in a conductor is given by i (5 + 16t) where t is in sec. Induced emf in it is 10 mv. Then: (a) Self inductance of coil is 62.5 mh. (b) Energy stored in inductor at t 1 sec is 0.14 J. (c) Power supplied to the coil at t 1 sec is 0.21 watt. (d) Power supplied to the coil at t 2 sec is 0.37 watt. 18. Figure shows a plane figure made of a conductor located in magnetic field along the inward normal to the plane of the figure. If the magnetic field starts diminishing, the induced current. (a) at point P is clockwise (b) at point Q is anti-clockwise (c) at point Q is clockwise (d) a point is zero 19. A bar magnet is pulled rapidly through a conducting coil along its axis with its south pole entering the coil first. Let, i, P and t denote the flux linked, induced current, rate of joules heating and time respectively, then: 20. The magnetic field perpendicular to the plane of conducting ring of radius r changes at the rate db. The: (a) Emf induced in the ring is r 2. (b) Emf induced in the ring is r (c) The potential difference between diametrically opposite points on the ring is half of induced emf. (d) All points on the ring are at same potential. 21. A conducting rod PQ of length l 1m is moving with uniform speed of 1m/s in a uniform magnetic field B 2T directed into the plane of paper. A capacitor of capacity 20 F is connected as shown in figure, then: (a) charge on capacitor is zero. (b) charge on capacitor is 40 C (c) A is at higher potential (d) B is at higher potential Passage: Consider a conducting circular loop placed in a magnetic field as shown. When magnetic field changes with time, magnetic flux also changes and emf is induced. e - d If resistance of loop is then induced current i e For current, charge must have come into motion. Magnetic force cannot make the stationary charges to move. Actually there is an induced electric field in the conductor caused by changing magnetic flux, which make the charges to move. E. dl e - d, This induced electric field is non-electrostatic by nature. Line integral of E around a closed path is non-zero.
22. The magnetic field within cylindrical region whose cross-section is indicated starts increasing at a constant rate tesla/sec. The graph showing the variation of induced electric field with distance r from the axis of cylinder is: 23. A square non-conducting loop, 20 cm. On a side is placed in a magnetic field. The centre of side AB coincides with the centre of magnetic field. The magnetic field is increasing at the rate of 2T/s. The potential difference between B and C is: (a) 10 mv (b) 20 mv (c) 30 mv (d) zero 24. efer to above question, the potential difference between C and D is: (a) 40 mv (b) 60 mv (c) 80 mv (d) zero 1. (a) As coils approach each other, the flux linked with each coil increases. A current will be induced in each coil which will try to decrease the flux. This implies induced current in each coil will be opposite to initial current. So, current in each coil decreases as the coils approach each other. Hence, choice (a) is correct and choice (b) is wrong. Choice (c) is wrong because if the coils move away from each other, the flux linked with each coil will decrease and induced current will try to increase the flux and hence current in each coil will increase. Choice (d) is wrong as explained above. 2. (c) When the rod is rotated clockwise, free electron in the rod also rotate clockwise. Since electrons are negatively charged, current associated with their motion will be anti-clockwise. According to Fleming s Left Hand ule, they experience a radically inward force and start to move from Q to P. Therefore, P becomes negatively charged and Q positively. It means potential of Q becomes higher than that of P. Hence, an electric field is established in the rod from higher to lower potential. Induced electric field in the rod is directed from Q to P. hence, choices (a) and (d) are wrong. Shifting of electrons continue till magnetic force e B is balanced by electric force. Suppose at distance x from P, electric field is E, then ee e (x ) B, or E B x It means electric field induced is not uniform but varies linearly from P to Q. Hence the electric field is non-uniform. Hence, choice (c) is correct and choice (b) is wrong. 3. (b) At a distance x, consider an element of length dx. Emf induced across two ends of small element dx is de B dx, de B x dx 4l/5 Hence, net emf between P and Q is E de B x dx l/5 E B l2 2 4l/5 l/5 B 2 [(4l 5 )2 - ( l 5 )2 ], B 2 [16l2 25 - l2 3 B l2 ] 25 10 4. (d) When a ring moves in a magnetic field perpendicular to its plane, replace the ring by a diameter perpendicular to the direction of motion. The emf is induced across this diameter. In the question, current flow in the ring will be through the two semiconductor portions, in parallel. Induced emf E B (2r), esistance of each half of ring /2 As they are in parallel, the equivalent resistance /4, i E /4, i B(2r) /4 So, current in the circuit 8Br, Choices (a), (b) and (c) are wrong. 5. (a) Due to current flowing in central wire, magnetic field lines are tangential to the coil. Hence, angle between B and area vector A is 90 0. Thus net flux passing through coil is always zero. Hence induced emf and induced current is zero. Choices (b), (c) and (d) are wrong. 6. (a) Let the uniform velocity be. Emf induced across the upper wire is Bl and current in the wire i Bl /, Magnetic force on the upper arm is F ilb B2 l 2 and acts in upward direction Mg B2 l 2 mg, or B 2 l 2, Since this frame moves with no acceleration. Choices (b), (c) and (d) are dimensionally wrong.
7. (b) Steady current i 24 2A, Final current is zero. Thus, di 12 E - L di 2A 2 X 10 3 s - 10 (- 1000) 10000 volt, Choices (a), (c) and (d) are wrong. - 1000 A/S 8. (b) When conductor moves with velocity, induced emf E Bl, E 2 X 1 X 2 4 volt Hence, across the rod PQ, induced emf 4 volt, Same potential difference of 4 volt is developed across the capacitor Q CV 10 X 10-6 X 4 40 C, From Fleming Left Hand ule, we can say that P is at a higher potential and Q is at a lower potential. This implies that plate A of capacitor is positive and plate B is negative. So, q A + 40 C, q B - 40 C. So choice (b) is correct and rest are wrong. 9. (d) Induced emf E - d - d (AB), Total emf 2 + 2 4 volt, E - A db, - (2)2 X (- 0.5) 2.0 volt Hence, choice (d) is correct and other choices are wrong. 10. (a) The ring may be considered as a circular loop made of wire of resistivity and area of cross section (dr X d) - r 2 B 0 cos t i E - d, E B 0 r 2 cos t esistance X r dr X d r2 db r2 d (B 0 sin t),, i B 0 d cos t r dr 11. (b) E - d, or 1 d E i, or d (i ), or i 10 X 1 X 5 X 0.1, 2.5 webers 2 12. (b) The time constant of the circuit is L 50 mh 10 5 ms, The current at time t is given by i i 0 (1 e -t/ ), or i 0 /2 i 0 (1 e -t/ ), e -t/ 1 2, or et/ 2, or t/ ln 2 or t ln 2, 5 ms X 0.693, t 3.5 ms, Hence, choice (b) is correct. 13. (d) When rings move, emf is induced in them. We can replace the induced emf by cells e 1 B 2r (), e 1 4 Br, e 2 B (4r), e 2 4 Br, V X V Z 4 Br, V Y V Z - 4 Br, (V X V Z ) (V Y V Z ) 4 Br + 4 Br or V X V Y 8 Br 14. (b,d) At time t, the distance travelled by the rod is ED t, tan AD or AD ED tan, AD t tan, tan (90 - ) DC or DC t cot ED ED So, AC AD + DC t (tan + cot ), Induced emf B l B (AC) B. t (tan + cot ), Induced emf B 2 t (tan + cot ), Hence, induced emf t and 2 15. (a, d) Because of larger loop, the field at the centre will be B 4 X 0 i (sin 4 ( L 2 ) 450 + sin 45 0 ) B 0 8 2 i, So, flux linked with the smaller loop, 4 L 2 BS 2 0 8 2 i 4 L l2 2 Mi 1, or Mi 0 8 2 i 4 L l2, or M 0 8 2 l 2, M l 2 4 L Hence, choice (a) is correct and choice b) is wrong. Also M 1 L Hence, choice (d) is correct and choice (c) is wrong. 16. (a, c) The initial velocity will produce an induced emf and hence an induced current in the circuit. The current carrying rod will now experience a magnetic force in opposite direction of its velocity. This force will retard the motion of conductor F m - ilb - (B l/) lb, m d - B2 l 2, d - B2 l 2 m d or - B2 l 2 t, Solving we get, mr 0 0 e B2 l 2 m.t This expression shows that velocity of rod decreases exponentially with time. Therefore, choice (a) is correct and choice (b) is wrong. Since i Bl /, i Bl 0 e B2 l 2 m.t, So, current in the circuit also because exponential with time. Hence, choice (c) is correct and choice (b) is wrong. 17. (a, b, c, d) E - L di, or 10 X 10-3 L d (5 + 16t), Solving, L 62.5 mh Hence, choice (a) is correct. Energy stored in inductor U 1 2 Li2, U 1 X 62.5 X 2 10-3 X (5 + 16t) 2 1 2 X 62.5 X 10-3 X (21) 2, U 0.14 J, Hence, choice (b) is correct. Power supplied to coil P Vi 10 X 10-3 (5 + 16t), at t 1, P 10 X 10-3 X 21 0.21 watt and at t 2, P 10 X 10-3 X 37 0.37 watt, Hence, choices (c) and (d) are wrong.
18. (a, b, d) Induced current in the diagram has been shown. We can see that at P the current is clockwise, at Q the current is anti-clockwise. At it is zero. The part connecting P and Q loops is shown in two parts. 19. (a, b, d) When magnet is moved towards the coil, the flux through the coil will increase non-linearly from zero to a maximum value and then will decrease as B 1 x3, Hence, choice (d) is correct. As induced emf e - d, - Slope of t curve, i e/ So emf e or current, will vary with time as shown in graph (b). Hence, choice (b) is correct. As P ei e 2 /, So power developed will be always positive. Hence, choice (c) is wrong and choice (d) is correct 20. (a, d) E d r2 db, or E r2, Hence, choice (a) is correct and choice (b) is wrong. Let i current in the ring, esistance of loop, Consider a small element dl of the ring. Emf induced in element de ( E ) dl, and resistance of element d ( ) dl r r Potential difference across the element dv de i d, ( E ) dl r (e) ( ) dl r dv zero, or V is constant. So, all points on the ring are at same potential. Hence, choice (c) is wrong and choice (d) is correct. 21. (b, c) Emf induced due to motion of conductor in magnetic field E Bl 2 X 1 X 1 2 volt Also charge on capacitor Q CV, 20 F X 2 volt, Q 40 C Hence, choice (b) is correct and choice (a) is wrong. Applying Fleming left hand rule on conductor PQ, we find the force on electron is towards Q. So, A is at higher potential and B is at lower potential. Hence, choice (c) is correct and choice (d) is wrong. 22. (a) For r <, E dl A db, E r ( r2 ), E r /2 or E r So, E-r graph is a straight line passing through origin. At r, E /2 For r >, E r ( 2 ), E 2 2r 23. (b) Perpendicular distance between BC and centre O is 10 cm. Component of induced electric field along the rod d 2 where d Perpendicular distance from centre to the rod. Hence, potential difference between the ends of rod or E 1 r V El l. d db, 10 X 2 2 10-2 X 20 X 10-2 X 2 20 mv 24. (a) Perpendicular distance between CD and O is 20 cm. Therefore, induced emf in CD d 2 l db 20 2 X 10-2 X 20 X 10-2 X 2, 40 mv db