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Electromagnetic Induction

Questions - Answers

Very Short Answer type Questions

1. Define magnetic flux?

A: The total number of lines of magnetic induction crossing any closed area is known as the magnetic flux linked with the given area.

2. State Faraday's law of electromagnetic induction.

A: Faraday's law: "The magnitude of the induced emf in the circuit is equal to the time rate of change of magnetic flux through the circuit".

 

3. State Lenz's law.

A: Lenz's law: The direction of induced emf is such as to oppose the change in magnetic flux that produces it.

4. Define Inductance.

A: Inductance is a coefficient of electromagnetic induction and is an intrinsic property of a material just like capacitance.

5. What do you understand by 'self  inductance'?

A:  The strength of current passing through the coil at any time (I)   the amount of magnetic flux linked with all the turns of the coil at that time.

Therefore, self inductance of a coil is numerically equal to the amount of magnetic flux linked with the coil when unit current flows through the coil.

6. Number of turns in a coil are 100. When a current of 5 A is flowing through the coil the magnetic flux is 10-16 Wb. Find self inductance of the coil.

 

7. What did the experiments of Faraday and Henry Show?

A: Faraday arrived at the following three conclusions.

(a) The galvanometer shows deflection only when there is a relative motion between the coil and the magnet.

(b) The direction of deflection (i.e. of induced current in the coil) is reversed if the direction of relative motion between the coil and the magnet is reversed.

(c) The deflection in the galvanometer increases if the magnet and the coil are rapidly moved w.r.t. each other.

8. What happens to the mechanical energy when a conductor is moved in a uniform magnetic field?

A: The mechanical energy spent in sliding the conductor is converted into electrical energy.

9. What are Eddy currents?

A: The induced circulating currents produced in a metal itself is due to change in magnetic flux linked with the metal are called eddy currents. These currents were discovered by Foucault, so they are known as Foucault currents. The direction of eddy currents is given by Lenz's law.

 

Short Answer type Questions
1. Obtain an expression for the emf induced across a conductor, which is moved in a uniform magnetic field which is perpendicular to the plane of motion.

A: Expression for induced emf:

 XPQY is a thick copper strip bent into shape as shown in figure. CD is thick copper wire resting on the arms PX and QY. The closed area is PCDQ.

 The magnetic field B is perpendicular to the plane PCDQ. When the wire CD moves with a velocity v, there is increase in area and increase in magnetic flux.

 

 Initial area = PCDQ; final area = PC'D'Q

Length of wire = AB = l; distance moved = dx;

Time taken = dt; Velocity of wire v = dx/dt.

 Change in area (dA) = PC'D'Q - PCDQ = CC'DD' = l × dx

Change in magnetic flux dφ = B (dA') = B (l × dx) = Bldx.

 

The -ve sign shows that the induced emf opposes the change in magnetic flux. Numerically E = Blv.

2. Obtain an expression for the mutual inductance of two coaxial solenoids.

A: Expression for mutual inductance of two coaxial solenoids:

 


 Consider two coaxial solenoids A & B. A is the primary solenoid and B is the secondary solenoid. It is assumed that there is no leakage of magnetic flux.

 Total number of turns of primary solenoid = N1

Area of cross section = A, length of primary coil = l

 

3. Obtain an expression for the magnetic energy stored in a solenoid in terms f the magnetic field, area and length of the solenoid.

A: Expresion for the magnetic energy stored in a solenoid:

1) Suppose the current "I" flowing through the inductor (coil) of inductance L.

 

 

This work done is stored as the energy in the magnetic field (UB).

 

6) If the solenoid of length l and area A is placed in uniform magnetic field B, hen B = µ0nI. Where n is number of turns per unit length.

 

4. Describe the ways in which Eddy currents are used to advantage.

A: Eddy currents are used to advantage in certain applications like:

a) Magnetic braking in trains: Strong electromagnets are situated above the ails in some electrical powred trains. When the electromagnets are activated, he eddy currents induced in the rails oppose the motion of the train. As there re no mechanical linkages, the braking effect is smooth.

b) Electromagnetic Damping: Certain galvanometers have a fixed core made of non magnetic metallic material. When the coil oscillates, the eddy currents enerated in the core oppose the motion and bring the coil to rest quickly.

c) Induction furnance: It can be used to produce high temparatures and can be utilised to prepare alloys, by melting the constituent metals. A high frequency alternating current is passed through a coil which surrounds the metals to be melted. The eddy currents generted in the metals produce high temperature sufficient to melt it.

d) Electric power meters: The shiny metal disc in the electric power meter rotate due to the eddy currents. Electric currents are induced in the disc by magnetic fields produced by similar varying currents in a coil. You can observe the rotating shiny disc in the power meter of your house.

e) Dia thermy: The statement of some of the diseases lies in warning the tissues. These tissues, which are lying deep in the body, cannot be supplied heat by ordinary methods. In such a case, a coil is wound around the part of the body to be treated. A high frequency (50 MHz) ac is passed through it and the heat produced due to the resulting eddy current goes to deep into the body.

Long Answer type Questions

1. Describe the working of a AC generator with the aid of a simple diagram and necessary expressions.

A: Alternating Current (ac) generator:
A generator is a machine used for generating electric current by converting electromagnetic mechanical energy into electrical energy using induction. When the current produced by a dynamo charges continuously in magnitude and periodically in direction, several times per second, the current is known as the alternating current and the machine which produces is called the a.c. generator.

Principle: In a closed circuit, the magnetic flux changes, an induced emf (e) is produced which lasts for the time the flux (fB) is changing.

 

Construction: It consists of the following four main parts.

i) Armature: Armature abcda (also called the coil) consists of a large number of turns of insulated copper wire wound over a soft iron core. It can revolve around an axle between the two poles of a strong magnet.

ii) Field Magnet: The magnetic field is supplied by a permanent magnet in small dynamos and by an electromagnet in the case of big (commercial) dynamos. The poles of the magnet are shown as N-S in the figure.

iii) Slip rings: R1 and R2 are two hollow metal rings held at different heights. The end 'C' of the armature coil is connected to the ring R1 . The end 'd' of the coil is passed through R1 without touching it and is connected to R2 these rings rotate with the rotation of the armature coil.

iv) Brushes (or) sliding contacts: B1 & B2 are two flexible metal plates or carbon rods. These are called brushes. B1 is in constant touch with R1 & B2 is in constant touch with R2. It is with the help of these brushes that the current is passed on from the armature and the rings to the external circuit of resistance R. Brushes are stationary i.e. they do not rotate with the rotation of the coil.

Working: The working of the ac generator will be clear from fig (a). As the armature coil is rotated, the magnetic flux linked with the coil changes. Therefore, an induced emf is developed in the armature coil. Let us suppose that the armature abcda is rotating clockwise. So that the arm ad moves inwards and bc moves outwards. Then applying Fleming's right hand rule, we see that the current flows in the armature as shown in figure.

2. Outline the path -breaking experiments of Faraday and Henry and highlight of contributions of these experiments to our understanding of electromagnetism.

A: Whenever there is a change in magnetic flux through a closed circuit, an induced emf is setup in the circuit. This phenomenon is known as electromagnetic induction. Faraday and Henry conducted a series of experiments to explain the electromagnetic induction.

I. Magnetic coil experiment:

1) The circuit consists a coil C1 connected in series with a galvanometer.

2) When the N-pole of magnet is moved towards the coil C1, the galvanometer shows deflection. The deflection shows there is current in the circuit.

3) When the N-pole of magnet comes to rest, the galvanometer shows no deflection.

4) The similar results are obtained when S-pole of a magnet is moved towards or away from the coil C1.

5) When the N-pole of magnet is moved away from coil C1, the galvanometer shows deflection in other direction.

6) When the magnet is moved fast, the deflection in the galvanometer is large & when it is moved slowly the deflection is small.

7) The induced current may be also produced by moving the coil C1 to a stationary magnet.

8) This experiment clearly demonstrate the electromagnetic induction. Whenever there is a relative motion between magnet & coils, the magnetic flux linked with coil changes and hence an induced current is produced due to which the galvanometer shows a deflection.

II. Coil -Coil experiment - Current induced by current:

1) As shown in fig. coil C1 is connected with galvanometer and coil C2 is connected with battery.

2) When the coil C2 is moved towards or away from C1, the galvanometer shows deflection due to current is produced in coil C1.

3) When the coil C2 is held fixed and Cis moved, the galvanometer shows deflection due to current induced in coil C1.

4) When two coils C1 & C2 are in relative motion, that induces electric curent.

III. Coil - Coil experiment - Current induced by changing current:

1) Two coils, C1 & C2 are held stationary, Coil C1 is connected to galvanometer G and coil C2 is connected to a battery through a tapping key K.

2) First, the battery circuit is closed by pressing the tap key K1 and then broken, the galvanometer shows deflection in one direction and then in the other.

3) When the key K is kept pressed continuously, there is no deflection in the galvanomter.

4) The deflection is produced in the galvanometer only at make or break of the current in the coil C2.

PROBLEMS

1. What happens to the mechanical energy when a conductor is moved in a uniform magnetic field?

 

Where B = uniform magnetic induction

l = length of conductor

v = velocity of conductor.

r = resistance of the rectangular loop

2. A long solenoid with 15 turns per cm has a small loop of area 2.0 cm2 placed inside the solenoid normal to the axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1s, what is the induced emf in the loop while the current is changing?

 

3. A jet plane is travelling towards west at speed of 1800 km/h. What is the voltage difference developed between the ends of the wing having a span of 25 m, if the earth's magnetic field at the location has a megnitude of 5 × 10-4 T and the dip angle is 30°.

 

e = ?, l = 25 m, R = 5.0 × 10-4 T and θ = 30°

e = Blv = Vlv, where v is vertical component of the earth's field.
             = (R Sin θ) lv = 5.0 × 10-4 × sin 30° × 25 × 500 = 3.1 Volt.

4. A square loop of side 10 cm & resistance 0.5 Ω is placed vertically in the east-west plane. A uniform magnetic field of 0.10 T is set up across the plane in the north-east direction. The magnetic field is decreased to zero in 0.70s at a steady rate. Determine the magnitudes of induced emf and current during this time interval.

A: The angle θ made by the area vector of the coil with the Magnetic field is 45°.

 

final flux, φmin = 0.

The change in flux is brought about in 0.70 s. From the magnitude of the induced emf is given by

5. A 10 m long metallic rod is rotated with an angular frequency of 400 rad s-1 about an axis normal to the rod passing out one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists every where. Calculate the e.m.f. developed between the centre and the ring

A: Here l = 1 m, ω = 400 s-1, B = 0.5 T, e = ?

Note that linear velocity of one end of rod is zero and linear velocity of other end

 

6. Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V induced, give an estimate of the self-inductance of the circuit

Posted Date : 30-09-2021

గమనిక : ప్రతిభ.ఈనాడు.నెట్‌లో కనిపించే వ్యాపార ప్రకటనలు వివిధ దేశాల్లోని వ్యాపారులు, సంస్థల నుంచి వస్తాయి. మరి కొన్ని ప్రకటనలు పాఠకుల అభిరుచి మేరకు కృత్రిమ మేధస్సు సాంకేతికత సాయంతో ప్రదర్శితమవుతుంటాయి. ఆ ప్రకటనల్లోని ఉత్పత్తులను లేదా సేవలను పాఠకులు స్వయంగా విచారించుకొని, జాగ్రత్తగా పరిశీలించి కొనుక్కోవాలి లేదా వినియోగించుకోవాలి. వాటి నాణ్యత లేదా లోపాలతో ఈనాడు యాజమాన్యానికి ఎలాంటి సంబంధం లేదు. ఈ విషయంలో ఉత్తర ప్రత్యుత్తరాలకు, ఈ-మెయిల్స్ కి, ఇంకా ఇతర రూపాల్లో సమాచార మార్పిడికి తావు లేదు. ఫిర్యాదులు స్వీకరించడం కుదరదు. పాఠకులు గమనించి, సహకరించాలని మనవి.

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