PREVIOUS YEAR QUESTIONS of ELECTROMAGNETIC INDUCTION for class 12

SANCHAY COACHING CENTRE

SCO 99, SECTOR 10A, GURGAON

Electromagnetic Induction – XII

1. A metallic rod of length l is rotated at a constant angular speed ω, normal to a uniform magnetic field B. Derive an expression for the current induced in the rod, if the resistance of the rod is R.
2. Derive an expression for the self-inductance of a long air cored solenoid of length l and number of turns N.
3. A coil of number of turns N, area A, is rotated at a constant angular speed ω, 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.
4. Define self-inductance. Write its SI unit.
5. (i) State Faraday’s law of electromagnetic induction (ii) A jet plane is travelling towards west at a speed of 1800 km/h. what is the Voltage developed between the ends of the wing having a span of 25m, if the Earth’s magnetic field at the location has a magnitude of 5 x 10^-4 T and the dip angle is 30^o.
6. (a) What are eddy currents? (b) Fig shows a rectangular conducting loop PQSR in which arm RS of length l is movable. The loop is kept in a uniform magnetic field B directed downwards perpendicular to the plane of the loop. The arm RS is moved with a uniform speed ‘v’. Deduce an expression for (i) the emf induced across the arm RS (ii) the external force required to move the arm, and (iii) the power dissipated as heat.
7. (a) State Lenz’s law. Give one example to illustrate this law. “The Lenz’s law is a consequence of the principle of conservation of energy.” Justify this statement. (b) Deduce an expression for the mutual inductance of two long coaxial solenoids but having different radii and different number of turns,
8. (i) State the law that gives the polarity of the induced emf. (ii) A 15 µF capacitor is connected to 220V, 50Hz source. Find the capacitive reactance and the rms current.

12. Two identical loops, one of copper and the other of Aluminium, are rotated with the same angular speed in the same magnetic field. Compare (i) the induced emf and (ii) the current produced in the two coils. Justify your answer.
13. Figure shown below shows a rectangular conductor PQRS in which the conductor PQ is free to move in a uniform magnetic field B perpendicular to the plane of the paper. The field extends from x = 0 to x = b and is zero for x > b. Assume that only the arm PQ possesses resistance r. When the arm PQ is pulled outwards from x = 0 to x = 2b and is then moved backwards to x = 0 with constant speed v, obtain the expressions for the flux and the induced emf. Sketch the variations of these quantities with distance 0 ≤ x ≤ 2b.
14. A rectangular loop and a circular loop are moving out of a uniform magnetic field to a field free region with a 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 filed region. The magnetic field is normal to the loops.
15. A current is induced in coil C₁ due to the motion of current carrying coil C₂. (i) Write any two ways by which a large deflection can be obtained in the galvanometer G. (ii) Suggest an alternative device to demonstrate the induced current in place of a galvanometer.
16. A magnet is quickly moved in the direction indicated by an arrow between the coils as shown in figure. What will be the direction of induced current in each coil as seen from the magnet? Justify your answer.
17. Write any two applications of eddy currents.
18. Derive the expression for energy stored in an inductor of self-inductance L.
19. A circular coil od 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.
20. A circular coil of closely wound N turns and radius r carries a current I. Write the expressions for the following: (i) the magnetic field at its centre (ii) the magnetic moment of this coil.
21. How can the self-inductance of a given coil having ‘N’ turns, area of cross section ‘A’ and length ‘l’ be increased?
22. When an ac source is connected across a capacitor, current starts is flowing through the circuit. Show how Ampere’s circuital law is generalised to explain the flow of current through the capacitor. Hence obtain the expression for the displacement current inside the capacitor.
23. A metallic rod held horizontally along east-west direction, is allowed to fall under gravity. Will there be an emf induced at its ends? Justify your answer.

23. The motion of the copper plate is damped when it is allowed to oscillate between the two poles of a magnet. What is the cause of this damping?
24. A capacitor, made of two parallel plates each of plate area A and separation d, is being charged by an external ac source. Show that the displacement current inside the capacitor is the same as the current charging the capacitor.
25. A wheel with 8 metallic spokes each 50 cm long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of the earth’s magnetic field. The earth’s magnetic field at the place is 0.4 G and the angle of dip is 60^o. Calculate the emf induced between the axle and the rim of the wheel. How will the value of emf be affected if the number of spokes were increased?
26. A light metal disc on the top of an electromagnet is thrown up as the current is switched on. Why? Give reasons.
27. How does the mutual inductance of a pair of coils changes when (i) distance between the coils is decreased and (ii) number of turns in the coil is decreased?
28. A coil of N turns and radius R carries a current I. it is unwound and rewound to make a square coil of side ‘a’ having same number of turns N. keeping the current I same, find the ratio of the magnetic moments of the square coil and the circular coil.
29. Starting from the expression for the energy W = ½ LI², stored in the solenoid of self-inductance L to build up the current I, obtain the expression for the magnetic energy in terms of the magnetic field B, area A and length ‘l’ of the solenoid having n number of turns per unit length. Hence show that the energy density is given by B²/2µ_o.
30. Two spherical bobs, one metallic and the other glass, are of same size are allowed to fall freely from the same height above the ground. Which of the two would reach earlier and why?
31. (a) Describe a simple experiment or activity to show that the polarity of emf induced in a coil is always such that it tends to produce a current which opposes the change of magnetic flux that produces it. (b) The current flowing through an inductor of self-inductance L is continuously increasing. Plot a graph showing the variation of (i) magnetic flux vs the current (ii) induced emf vs dI/dt (iii) magnetic potential energy stored vs the current.
32. A metallic piece gets hot when surrounded by a coil carrying high frequency alternating current. Why?
33. In an experiment, two coils C₁ and C₂ are placed close to each other. Find out the expression for the emf induced in the coil C₁ due to change in the current through the coil C₂.
34. Define mutual inductance and write its SI units.
35. When an ideal capacitor is charged by a dc battery, no current flows. However, when an a.c. source is used, the current flows continuously. How does one explain this, based on the concept of displacement current?