Electromagnetic Induction-05-SUBJECTIVE LEVEL - I (C.B.S.E.)

SUBJECTIVE LEVEL - I (C.B.S.E.) (REVIEW YOUR CONCEPTS) 1. Figure below shows planer loops of different shapes moving out of or into a region of a magnetic field which is directed normal to the plane of the loop away from the reader. Determine the direction of induced current in each loop using Lenz’s Law. 2. Predict the direction of induced current in the situations described by the following figures. 3. Use Lenz’s law to determine the direction of induced current in the situations described by figure. (a) A wire of irregular shape turning into a circular shape. (b) A wire of rectangular shape turning into a circular shape. 4. A small piece of metal wire is dragged across the gap between the pole pieces of a magnet in 0.5 s. The magnetic flux between the pole pieces is known to be 8 × 10-4 Wb. Estimate the emf induced in the wire. 5. A long solenoid with 15 turns per cm has a small loop of area 2.0 cm2 placed inside normal to the axis of the solenoid. If the current carried by the solenoid changes steadily from 2 A to 4 A in 0.1 s, what is the induced voltage in the lop while the current is changing ? 6. A 1 m long conducting rod rotates with an angular frequency of 400 s-1 about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the center and the ring. 7. A circular coil of radius 8.0 cm and 20 turns rotates about its vertical diameter with an angular speed of 50 s-1 in a uniform horizontal magnetic field of magnitude 3 × 10-2 T. Obtain the maximum and average emf induced in the coil If the coil forms a closed loop of resistance 10  , how much power is dissipated as heat ? What is the source of this power ? 8. A wheel with 10 metallic spokes each 0.5 m long is rotated with a speed of 120 rev/min in a plane normal to the Earth’s magnetic field at the place. If the magnitude of the field is 0.4 G, what is the induced emf between the axle and the rim of the wheel ? 9. Two solenoid of equal length and almost equal cross-sectional area are fully inserted into one an- other. Find their mutual inductance if their inductances are equal to L1 and L2. 10. Two thin concentric wires shaped as circles with radii a and b lie in the same plane. Allowing for a << b, find their mutual inductance. 11. A square loop of side 12 cm with its sides parallel to X and Y axes is moved with a velocity of 8 cm s-1 in the positive x-direction in an environment containing a magnetic field in the positive z-direction. The field is neither uniform in space nor constant in time. It has a gradient of 10-3 T cm-1 as one moves in the negative x-direction (that is it increases by 10-3 T cm-1 as one moves in the negative x- direction), and it is decreasing in time at the rate of 10-3 T s-1. Determine the direction and magnitude of the induced current in the loop if its resistance is 4.5 m . 12. It is desired to measure the magnitude of field between the poles of a powerful loud speaker magnet. A small flat search coil of area 2 cm2 with 25 closely wound turns, is positioned normal to the field direction, and then quickly snatched out of the field region. Equivalently, one can give it a quick 90º turn to bring its plane parallel to the field direction). The total charge flown in the coil (measured by a ballistic galvanometer connected to coil) is 7.5 mC. The resistance of the coil and the galvanometer is 0.50  . Estimate the field strength of magnet. 13. An air-cored solenoid with length 30 cm, area of cross-section 25 cm2 and number of turns 500, carries a current of 2.5 A. The current is suddenly switched off in a brief time of 10-3 s. How much is the average back emf induced across the ends of the open switch in the circuit ? Ignore the variation in magnetic field near the ends of the solenoid. 14.(a) Obtain an expression for the mutual inductance between a long straight wire and a square loop of side a as shown in figure. (b) Evaluate the induced emf in the loop if the wire carries a current of 50 A and the loop has an instantaneous velocity  = 10 m s-1 at the v location x = 0.2 m, as shown. Take a = 0.1 m and assume that the loop has a large resistance. 15. A line charger  per unit length is pasted uniformly onto the rim of a wheel of mass M and radius R. The wheel has light non-conducting spokes and is free to rotate about a vertical axis as shown in figure. A uniform magnetic field extends over a radial region given by, →  B kˆ ( r  a; a  R ) B 0 = 0 (otherwise) R What is the angular velocity of the wheel when this field is suddenly switched off ?