Bihar Board - Class 12 Physics - Chapter 6: Electromagnetic Induction Long Answer Question
Long Answer Type Questions
1. (i) How is magnetic flux linked with the armature coil changed in a generator ?
(ii) Derive the expression for maximum value of the induced emf and state the rule that gives the direction of the induced emf.
(iii) Show the variation of the emf generated versus time as the armature is rotated with respect to the direction of the magnetic fields.
Answer:
(i) The direction of flow of current in resistance R gets changed alternatively after every half cycle.
Thus, AC is produced in coil.
(ii) Let at any instant total magnetic flux linked with the armature coil is G. and θ = ωt is the angle made by the area vector of the coil with magnetic field.
Φ = NBA cosθ = NBA cosωt
ddt = -NBAω sin ωt
- ddt = NBAω sin ωt
By Faraday’s law of emf, e = - ddt
Induced emf in coil is given by,
e = NBAω sinωt
e = e0 sinωt
where, e0 = NBAω = peak value of induced emf
(iii) The mechanical energy spent in rotating the coil in the magnetic field appears in the form of electrical energy.
2. Define the coefficient of self inductance. Write its unit. Give two factors on which the self-inductance of a long solenoid depends.
Answer: From self induction, we know that if I is the strength of the current flowing through a coil at any time ϕ is amount of magnetic flux linked with the coil at that time.
It is found that
ϕ ∝ Or, ϕ LI …(i)
L is a constant of proportionality and is called coefficient of self induction or self inductance of the coil.
The value of L depends upon the number of turns of the coil, area of cross-section and nature of material of the core on which coil is wound.
If I = I, ϕ = L or L = ϕ
Therefore, the coefficient of self-induction of a coil is numerically equal to the amount of magnetic flux linked with the coil when unit current passes through the coil.
The unit of coefficient of self induction is Henry.
Self inductance of a long solenoid depends upon the following factors (i) directly proportional to the area of the cross-section of the solenoid and (ii) inversely proportional to the length of the solenoid.
3. How does the mutual inductance of a pair of coils get affected when
(i) distance between coils is increased?
(ii) the number of turns in each coil is decreased?
(iii) a thin iron sheet is placed between the two coils, other factors remaining the same? Explain your answer in each case?
Answer:
(i) Mutual inductance decreases with the increase of distance between the coils. This is due to loose coupling between the coils.
(ii) With the decrease of the number of turns, the mutual inductance decreases. The coupling between two coils is proportional to np ns, where np and ns are the number of turns in primary and secondary coils respectively. Hence mutual inductance decreases with the decrease in number of turns of the two coils.
(iii) When a thin iron sheet is placed between the two coils the permeability of the medium is increased many times, which results in increase of mutual inductance between the coils.
4. A conducting circular loop is placed in a uniform magnetic field B = 0.025 T with its plane perpendicular to the field. The radius of the loop is made to shrink at a constant rate 1 mm s-1. The induced e.m.f. when the radius is 2 cm is ?
Solution: Given : B = 0.025 T
R = 2 cm
dR/dt = 1 mms-1
The direction of B and A is same
|E| = |-dϕ/dt|
E = dϕ/dt
E = d (BA cos 0)/ dt
E = B cos0 dA/dt
E = B d(πR2)/ dt
E = B π(2R) dR/dt
E = 0.025 × π × 2 × 2 × 10-4 × 1 × 10-3
E = π × 10-6 V
E = π μV
5. What are the advantages or application of eddy currents ?
Answer: Following are the advantages of eddy currents :
(i) Diathermy : These are used for deep heat treatment i.e., localized heating of tissues in the human body. This treatment is called Diathermy.
(ii) Concept of eddy currents is used in energy meters to record the consumption of electricity.
(iii) Speedometer : The eddy currents are produced in the aluminum drum in which a magnet attached to the axle of the wheel rotates according to the speed of the vehicle. The pointer attached to the drum is deflected in the direction of rotation of the drum.
(iv) Electromagnetic brakes : These are used in trains. The large eddy currents are produced in the metallic drum which oppose the motion of the drum.
(v) Dead beat galvanometer : Electromagnetic damping is used to stop coils in a shorter interval of time. When the coil wound over a metallic frame is deflected, eddy currents are produced in the metallic frame which oppose the motion of the coil.
(vi) Induction Furnace makes use of the heating effect of eddy currents.
(vii) Induction motor or a.c. the motor also works by eddy currents.
6. What are eddy currents? Write their two applications.
Answer: Eddy Current: Eddy currents are the currents induced in the bulk pieces of conductors when the amount of magnetic flux linked with the conductor changes.
Eddy currents can be minimized by taking a laminated core, consisting of thin metallic sheets insulated from each other by varnish instead of a single solid mass. The plane of the sheets should be kept perpendicular to the direction of the currents. The insulation provides high resistance hence, eddy current gets minimized.
Applications :
(i) Electromagnetic damping
(ii) Induction furnace.
7. A magnetic field of 2 × 10-2 T acts at right angles to a coil of area 100 cm2 with 50 turns. The average e.m.f. induced in the coil is 0.1v, when it is removed from the field in the time t. the value of t is ?
Solution: Given – N = 50
B = 2 × 10-2 T
A = 100 cm2
E = 0.1 v
|E| = |-dϕ/dt|
|E| = |ϕ2 – ϕ1/dt|
dt = |0 – NBA cos 0 / 0.1| -------------------------- 0˚ because it acts as a right angle of a coil
dt = |0 – 50 × 2 ×10-2× 100 × 10-4 cos 0/ 0.1|
dt = 0.1 s
8. State and explain Faraday’s laws of electromagnetic induction.
Answer: First law : Whenever the amount of magnetic flux linked with a circuit changes, an e.m.f. is induced in the circuit. The induced e.m.f. lasts so long as the change of magnetic flux continues.
Explanation. When a magnet is moved towards or away from a coil, the number of magnetic lines linked with the coil increases and vice versa. In both cases, the galvanometer put in the circuit shows deflection. When there is no relative motion between magnet and coil, no deflection in the galvanometer is observed since the magnetic field in this case is constant.
Second law: The magnitude of e.m.f. induced in a circuit is directly proportional to the rate of change of magnetic flux linked with the circuit.
Explanation. In Faraday’s experiment, if we move the magnet faster, more deflection will be obtained in the galvanometer. Again, more deflection will be obtained if we move a stronger magnet. This shows that e.m.f. induced is proportional to the rate of change of magnetic flux.
9. What is mutual induction? Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation I = l0 Sin ωt, where l0= 10 A and ω = 100 π rad-1 . Then what is the maximum value of e. m. f. in the second coil ?
Answer:
Mutual inductance – When two coils are brought in proximity with each other then the magnetic field in one of the coils tends to link with the other coil. This leads to generation of voltage in the second coil. This property of the coil that affects or changes the current and voltage in the secondary coil is called mutual inductance.
Given – M = 0.005 H
l0 = 10 A and ω = 100 π rad-1
E = |M dI/ dt|
E = |M d l0 Sin ωt / dt|
E = 0.005 × l0 cos ωt × ω
Emax = 0.005 × l0 × ω
Emax = 0.005 × 10 × 100π
Emax= 5π
10. Show that Lenz's law is a direct consequence of the law of conservation of energy.
Or
What is Lenz’s law? Show that it is in accordance with the law of conservation of energy.
Answer:
Lenz’s law: It states that the direction of induced e.m.f. is such that it always opposes the cause which produces it.
Lenz’s law obeys the law of conservation of energy.
When the N pole (or S pole) of a magnet is moved towards a coil, the induced current is produced in the coil and it makes the front face of the coil a north pole (or south pole). Thus a force of repulsion between the magnet and the coil takes place. To overcome this force of repulsion, some work has to be done against the force of repulsion. This mechanical work is converted into electric energy. Hence Lenz's law is in accordance with the law of conservation of energy.
11. Define mutual inductance. State two factors on which the mutual inductance between a given pair of coils depends.
Answer: Mutual inductance is the property of two coils by virtue of which each opposes any change in the strength of the current flowing through the other by developing an induced e.m.f.
Coefficient of mutual inductance of two coils is numerically equal to the amount of magnetic flux linked with one coil when unit current flows through the neighboring coil.
Mutual inductance depends upon:
Geometry of coils i.e. number of turns, nature of the material on which wound; size and shape of the coils.
distance between two coils.
Orientation or relative placement of the coils.
12. 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 x 10-4 Wb m-2.
(a) What is the instantaneous value of the emf induced in the wire?
(b) What is the direction of the emf?
(c) Which end of the wire is at the higher electrical potential?
Solution:
Here, length of the wire, 1 = 10m;
Velocity of the wire, V = 5.0 ms-1
Horizontal component of earth’s magnetic field,
BH = 0.30 x 10-4 Wbm-2
(a) Now,e = BHlV = 0.30 x10-4 x 10 x 5.0 = 1.5 x 10-3 V
(b) The induced e.m.f. will be set up from west to east end.
(c) The eastern end will be at higher potential.
13. Write the application of eddy current .
Answer: Application of eddy currents. Eddy currents have been put to the following important uses:
1. Speedometers. In a speedometer, a drum rotates according to the speed of the vehicle. The magnet is placed inside an aluminum drum which is carefully pivoted. When the magnet swings, it drags the drum also through a certain angle depending upon the speed of the vehicle.
2. Induction furnace. A metallic substance which is to be melted is placed in a high frequency magnetic field. Large eddy currents will be produced in the substance and so much heat is produced that it melts the substance. This arrangement is used to separate metal from its ore and some alloys of metal can be formed.
3. Dead beat Galvanometer. When steady (constant) current is passed through the coil of a galvanometer, it is deflected and oscillates about its equilibrium position for a long time. But if the same coil is wound over a metallic frame and as current is passed in the coil, eddy currents are produced in the metal frame which opposes the motion of the coil and makes it deadbeat i.e. non-oscillatory. This is also called electromagnetic damping.
4. Damping. To stop the vibrations of the ballistic galvanometer, the galvanometer is shunted by connecting external shunt resistance across the whole of the coil. Smaller the shunt, greater are the eddy currents. The eddy currents thus damp the motion of ballistic galvanometers.
5. Induction motor. In an a.c. induction motor, a metallic cylinder is placed in the rotating magnetic field. Eddy currents are produced in the cylinder which try to decrease the relative motion between the rotating magnetic field and the cylinder. As a result, the cylinder also starts rotating about its axis.
6. Magnetic brakes. When a train moves, the axis of the wheel also rotates. A drum attached to the axle also starts rotating. Whenever the train is required to be stopped, a magnetic field is applied to the rotating drum. The eddy current production in the drum apply upon it an opposing torque and as a result the train stops immediately.
14. Suppose a helical spring is suspended from the roof and a very small weight is attached to its lower end. What will happen to the spring when the current is passed through it? Give reason to support your answer.
Answer: The spring will contract.
Reason: We know that if current passes through a wire in clockwise direction, it behaves like the South pole and if it flows in anticlockwise direction, it behaves like North pole.
If we observe the enclosed figure, the current is flowing in an anticlockwise direction when observed from above and clockwise if observed from below. Hence the upper side will behave like the north and lower like the south pole. Whole of the coil will behave like N and S poles placed side by side and hence will attract each other resulting in contraction of the coil.
15. Describe construction of a.c. generator.
Answer: a.c. generator or dynamo : It is an electric instrument which converts mechanical energy into electrical energy. It is mainly based on the principle of electromagnetic induction.
The transformation of mechanical energy to electrical energy takes place in the form of a.c.
Construction : The apparatus has been shown in fig. It has following main parts :
(i) Field magnet : There are two pole pieces of a strong magnet face to face. An uniform magnetic force field is produced between poles.
(ii) Armature : It is made by winding a copper coil (ABCD) on a cylindrical core of soft iron. It is fitted with an insulated axle which is rotated between N & S by an instrument.
(iii) Slipy rings : There are two rings R, & R, on axles to which two ends of the armature are joined separately. When the axle rotates then rings move with armature.
(iv) Brush : Two brushes B, and B, of carbon touch the two rings R, & R..
16. A current is induced in coil C1 due to the motion of current carrying coil C2.
(a) Write any two ways by which a large deflection can be obtained in the galvanometer G.
(b) Suggest an alternative device to demonstrate the induced current in place of a galvanometer .
Answer:
(a) To obtain a large deflection, one or more of the following steps can be taken :
Use a rod made of soft iron inside the coil C2.
Connect the coil to a powerful battery.
Move the arrangement rapidly towards the test coil C1
(b) Replace the galvanometer by a small torch bulb.
17. (a) Define self-inductance of a coil and hence write the definition of ‘Henry’.
(b) Write any two factors each on which the following depends :
(i) Self inductance of a coil.
(ii) mutual inductance of a pair of coils.
Answer:
(a) The self-inductance (L) of a coil equals the magnetic flux linked with it, when a unit current flows through it.
One henry is the self inductance of a coil for which the magnetic flux, linked with it, due to a current of 1A, flowing in it, equals one weber.
(b) (i) Self inductance of a coil depends on
Its geometry (area and length of a coil.
Number of turns
Medium within the coil
(ii) Mutual inductance of a given pair of coils depends on
Their geometries
Their distance of separation
Number of turns in each coil.
Nature of medium in the intervening space.
18. State Lenz’s law. Explain, by giving examples, that Lenz’s law is a consequence of conservation of energy.
Answer: Lenz’s law states that “The polarity of induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produced it.”
As shown in the diagram (a) given, when the north pole of a bar magnet is pushed towards the close coil, the magnetic flux through the coil increases and the current is induced in the coil in such a direction that it opposes the increase in flux. This is possible when the induced current in the coil is in the anticlockwise direction.
Similarly as shown in the diagram (b), just the opposite happens when the north pole is moved away from the coil.
In either case, it is the work done against the force of magnetic repulsion or attraction that gets ‘converted’ into the induced emf.
19. State Faraday’s laws of electromagnetic induction.
Answer: First law. Whenever the amount of magnetic flux linked with a circuit changes, an e.m.f. is induced in the circuit. The induced e.m.f. lasts so long as the change in the magnetic flux continues.
Second law. The magnitude of e.m.f. induced in the circuit is directly proportional to the rate of change of magnetic flux linked with the circuit.i.e.
e ∝ 2 - 1t
e = -k ddt
e = - ddt ∵ k =1
-ve sign means opposing nature of induced e.m.f.
20. Explain the production of eddy currents in a conductor.
Answer: When a plate or anybody made of metal is moved in or out of a magnetic field or placed in any changing magnetic field, the amount of the flux linked with the plate changes and an induced e.m.f. is
developed on the plate. The induced e.m.f. causes currents which flow in many closed paths throughout the body of the conductor in the same way as in a closed circuit placed in a varying magnetic field. Such currents are known as eddy currents. They are so called because they look like eddies or whirlpools. Eddy currents are used for making moving coil galvanometer dead beat. It is also used in induction motors, magnetic brakes, speedometer and induction furnaces etc.
21. Twelve wires of equal lengths are connected in the form of a skeleton cube which is moving with a velocity v in the direction of magnetic field v. Find the e.m.f. in each arm of the cube.
Answer:
The induced e.m.f. is given by
e = Blv sin θ
For horizontal conductors, θ = 0, so e = 0
Now the magnetic flux produced in the vertical conductors passes through the empty portion of the coil and hence no induced e.m.f. is produced.
22. Explain self – induction and demonstrate the phenomenon by an experiment.
Answer: Self – induction:
During the motion of the truck, the axle cuts the magnetic flux of the earth, which causes an induced e.m.f. set up across its axle. These induced charges are earthed by the chain. Which prevents the explosive from the fire.
Experiment:
The circuit of the experiment is shown in the figure. It consists of an insulated copper coil L, wound on a soft iron core. Cell E, rheostat Rh and a tapping key K are connected in series. A bulb B is connected in parallel with the coil. Now, the key is closed, the bulb glows slowly, then becomes bright and when it is opened, the bulb flashes bright and then goes off.
As the key is pressed, the flux linked with coil changes and an induced current flows in the opposite direction of main current, because of this the current grows slowly in the circuit.But when the key is opened, the flux suddenly decreases to zero, therefore a strong induced current flows in the same direction of circuit current makes the bulb very bright for a moment.
23. What are eddy currents? Show an experiment to demonstrate eddy currents.
Or
What are eddy currents? What are their disadvantages ? Write any two uses of eddy currents.
Answer: Eddy currents:
When a metallic plate is moved in a magnetic field or placed in a changing magnetic field, then flux linked with the conductor changes, hence an induced current is produced in the plate. This induced current is called eddy current.
Demonstration:
A rectangular copper plate is free to oscillate about a horizontal axis, passing through O. It is placed between the pole pieces of an electromagnet NS. Oscillate the plate, when no current is flowing in the circuit, the plate will oscillate for a long time and due to air resistance finally its amplitude of oscillation decreases.
Now, oscillate and pass the current. It is observed that the oscillations of the plate will be damped soon. Just as eddies are produced on water surface, the change of flux through the metal plate develops induced currents known as eddy currents.
Uses : Eddy currents are used in :
Making a galvanometer dead beat.
Induction furnace.
Electric break.
Induction motor, etc.
Disadvantages of eddy currents:
Production of eddy currents causes loss of electrical energy in the form of heat. In order to prevent this, a soft-iron core is laminated in a transformer. Lamination increases resistance and decreases eddy currents. So, there is very little dissipation of electrical energy in the form of heat.
24. A current is flowing through a coil having 800 turns. The flux linked with it is 1.5 x 10-5 Wb. Find the self-inductance of the coil.
Solution: Formula : = LI
Flux linked with one turn = 1.5 x 10-5 Wb,
∴ Flux linked with 800 turns = 800 x 1.5 x 10-5 Wb
Substituting the values, we get
800 x 1.5 x 10-5 = L x 1.5
∴ L = 800×10-5
= 8.0 x 10-3 H
= 8.0 mH.
25. (a) An induced EMF has no directions of its own. Explain why.
(b) From where does the energy for induced current come from?
Answer:
(a) As per Lenz's law the direction of induced EMF for current is such that it opposes the very cause which produces the EMF. If in a circuit current (flux) is increasing, the induced EMF or current tends to oppose the growth of current. On the other hand, if current is failing in a circuit, the induced EMF or current tends to oppose the fall in current. Thus, it is self-evident that induced EMF has no definite directions of its own.
(b) The electrical energy due to production of induced EMF for current comes at the expense of an equal amount of mechanical energy. When a magnet is brought towards a coil or a coil is rotated in a uniform magnetic field or a conductor road is moved in a uniform magnetic field, etc., some mechanical work has to be done on the magnetic or coil or conductor rod, etc. As a result of this, mechanical work done, an electrical emf current is induced.
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