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21. There will be no emf induced in the conductor as the Lorentz force acting on the charges (free electrons) in the conductor will be zero and hence, no displacement of charges towards the ends will take place.


22. The emf induced in the loops will be same as they are rotated with the same speed in the same magnetic field. But induced current will higher in the loop having smaller resistance. For identical loops, copper loop will have smaller resistance. So, the loop in which the induced current is 2 A is made of copper wire.


23. The magnetic flux linked with the loop changes as the magnet falls freely through it. Thus, an emf is induced in the loop, but there will be no induced current as it has a cut in it. Therefore, there will no force opposing the motion of the magnet and acceleration of the magnet will be equal to g.


24. No, there will be no induced current in the loop because the rotation of the magnet about its axis does not change the flux.


25. There will be no motional emf induced in the rod because ebonite is an insulator. When it is moved in the field, charges will not be displaced to produce motional emf.


26. Yes, an emf will be induced across the axle as an axle moving in the horizontal plane cuts the vertical component of earth's magnetic field.


27. If a conducting rod PQ lying parallel to y-axis starts moving in z direction at constant speed in a uniform magnetic field pointing in the positive x direction, the magnetic force will act on free electrons towards end P according to Fleming's left hand rule. Therefore, end P of the rod gets negatively charged.


28. Yes, the ring will move away from the magnet due to induced current.


29. When the magnetic field is switched on, the flux linked with the bob changes and consequently eddy currents are produced in it which opposes its motion. Thus, the oscillations are damped and die out quickly.


30. When the ball is dropped into the space between the poles of the electromagnet and the magnet is switched on, strong eddy currents are set up in it. These currents oppose the motion of the ball according to Lenz's law and hence, the ball falls as if it is passing through a viscous liquid.


31. An ideal inductor has zero resistance. But every inductor has some resistance due to the wire making it.


32. The emf induced in the inductor delays the growth of the current. The time taken the reach the final value depends on the time constant (L/R) of the RL circuit. The final current in the RL circuit is given by emf/R. When the current stops changing, the emf induced in the inductor becomes zero. Thereafter, the inductor behaves like a conductor of zero resistance when the current reaches its final value.


33. A coil having large number of turns has sufficient inductance. Therefore, an emf is induced in the coil when the circuit is switched on. The emf induced in the coil delays the growth of current in the circuit. Consequently, the bulb takes some time before it glows with full brightness.


34. The resistance of an inductive coil should be as small as possible. The resistivity (or specific resistance) of the copper is small. Hence, it is used for making coils.


35. Mutual inductance between two coils is a measure of the magnetic flux of one coil that links with the other adjacent coil and vice versa. If the magnetic fluxes of two coils aid each other, the inductance of each coil increases by the mutual inductance M and if the fluxes of two coils oppose each other, the inductance will decrease by M.


36. 1. When the distance between the two coils is increased, the flux passing through one coil due to the other decreases. As a result of this, the mutual inductance of the pair of coils decreases.
    2. It is clear from the formula of mutual inductance that if the number of turns in each coil is decreased, the mutual inductance decreases.
    3. It is clear from the formula of mutual inductance that M depends on relative permeability. So, when a thin iron sheet is placed between the two coils, M increases as iron has large μ_r .


37. 1. Self-induction is the phenomenon in which an emf is induced in a circuit when a current passing through it changes. On the other hand, mutual induction is the phenomenon in which an emf is induced in one circuit when the current in the neighbouring circuit changes.
    
    
    2. Self-inductance of a coil depends upon the size, shape and the number of turns of the coil. Mutual inductance of two coils depends on the number of turns in the two coils, their shape and relative separation.


38. In a dc circuit, the resistance of a solenoid (inductor) is zero. When an iron rod is inserted into the solenoid, its inductance increases but the resistance remains the same. Therefore, the brightness of the bulb does not change when the iron rod is inserted.


39. A ferromagnetic material such as a soft iron moves from weaker to stronger magnetic field. The magnetic field at the centre of the current carrying solenoid is greater than that at its value at the ends. Therefore, a soft iron rod will be pulled from the end to the centre of the solenoid.


40. The factors upon which the induced emf depends are the number of turns, angular velocity, area of the area and the strength of the magnetic field.


41. The maximum emf produced in a generator is given by ε₀ = NAB ω₀. When the speed of rotation (ω₀) of the armature is increased,
    1. the maximum e0 increases
    2. the frequency (f) of the emf also increases as it is same as the frequency of rotation of the armature.

CBSE Electromagnetic Induction ( With Hint / Solution)
Class XII (By Mr. Ashis Kumar Satapathy)
email - [email protected]

Electromagnetic Induction