NCERT 12 Physics Electromagnetic Induction Chapter 6 Exercise

Q.1. Predict the direction of induced current in the situations described by the following (a) to (f).

Q.2. Use Lenz’s law to determine the direction of induced current in the situation described

(a) a wire of irregular shape turning into a circular shape (b) a circular loop being deformed into a narrow straight were. The crosses indicate the magnetic field into the paper and the dots indicate magnetic field out of the paper.

Q.3. A long solenoid with 15 turns per cm has 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 loop, while the current is changing ?

Q.4. A rectangular loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 tesla directed normal to the loop. What is the voltage developed across the cut if velocity of loop is 1 cm s^-1 in a direction normal to the (i) longer side (ii) shorter side of the loop ? For how long does the induced voltage last in each case?

Q.5. A 1m long conducting rod rotates with an angular frequency of 400 red 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 ting. A constant magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the e. m. f. developed between the Centre and the ring.

Q.6. 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 e. m. f. induced in the coil. If the coil forms a closed loop resistance 10 Ω, calculate the maximum value of current in the coil. Calculate the average power loss due to joule heating. Where does this power come from ?

Q.7. A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5-0 ms^-1 at right angles to the horizontal component of the earth’s magnetic field 0.30×10^-4 Wb m².

(a) What is the instantaneous value of the e. m. f. induced in the were?

(b) What is the direction of e. m. f. (c) Which end of the wire is at higher electric potential?

Q.8. Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average e. m. f. of 200 V is induced, give an estimate of the self inductance of the circuit ?

Q.9. A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change in flux linkage with the other coil ?

Q.10. A jet plane is travelling west at the speed of 1800 km/h. What is the voltage difference developed between the ends of the wing 25 m log, if the earth’s magnetic field at the location has a magnitude of 5.0×10^-4  T and the dip angle is 30⁰ ?

Q.11. Suppose the loop in Q.4 is stationary, bot the current feeding the electromagnet that produces the magnetic filed is gradually reduced so that the field decreases from its initial value of 0.3 T at the rate of 0.02 T/sec. If the cut is joined and loop has a resistance of 1.6  how much power is dissipated by the loop as heat ? What is the source of this power ?

Q.12. A square loop of side 12 cm with its sides parallel to X and Y axis is moved with a velocity of 8  cm s^-1 in the positive X direction in 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 along the negative x direction (i. e. it increases by 10^-3 T cm^-1 as one moves in 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 Ω.

Q.13. It is desired to measure the magnitude of field between the poles of a powerful loud speaker magnet. A small flat search coil of are 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 90⁰ turn to bring its plane parallel to field direction). The total charge flowing in the coil (measured by a ballistic galvanometer connected to the coil) is 7.5 m C. The resistance of the coil and galvanometer is 0.5 Ω. Estimate the field strength of the manet.

Q.14. shows a metal rod PQ resting on the rails  A, B and positioned between the poles of a permanent magnet. The rails, the rod and the magnetic field are in three mutually perpendicular directions. A galvanometer connects the ails through a switch K. Length of the rod = 15 cm,  B = 0.50 T, resistance of closed loop containing the rod = 9.0 m . Answer the followi0 ng questions :

(a) Suppose K is open and the rod moves with a speed of 12 cm/s in the direction shown. Give the polarity and magnitude of induced e. m. f.

(b) Is there an excess chare built up at the ends of the rods when K is open ? What if K is closed?

(c) With K open and the rod moving uniformly, there is no net force on the electron in the rod PQ even though they do experience magnetic force due to the motion of the rod. Explain.

(d) What is the retarding force on the rod when K is closed ?

(e) How much power is required (by an external agent) to keep the rod moving at the same speed (=12 cm/s) when K is closed.

(f) How much power is dissipated as heat in the closed circuit ? What is the source of this power ?

(g) What is the induced e. m. f. in the moving rod when the permanent magnet is rotated to a vertical position so that the field is parallel to the rails instead of being perpendicular ?

Q.15. 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 e. m. f. induced across the ends of the open switch in the circuit? Ignore the variation in magnetic field near the ends of the solenoid.