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Physics · Class 12 Science

Ch 6Electromagnetic Induction — Class 12 Physics, concept-first.

For a long time, electricity and magnetism were treated as two completely separate phenomena. This changed in the early 1800s, when Oersted, Ampere, and others showed through experiments on electric current that the two are related: moving electric charges produce magnetic fields.

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Electromagnetic Induction

Electromagnetic induction is the phenomenon in which a changing magnetic flux through a circuit produces an electromotive force (emf) — and hence a current, if the circuit is closed.

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

6.1

Introduction

For a long time, electricity and magnetism were treated as two completely separate phenomena. This changed in the early 1800s, when Oersted, Ampere, and others showed through experiments on electric c…

6.2

The Experiments of Faraday and Henry

The experiments of Faraday and Henry reveal a fundamental principle: a changing magnetic field can induce an electric current in a nearby conductor.

6.3

Magnetic Flux

Faraday’s experiments revealed that a changing magnetic environment induces an electric current. The key to quantifying this change is magnetic flux ().

6.4

Faraday's Law of Induction

Faraday’s experiments showed that an electromotive force (emf) is induced in a circuit only when the magnetic flux through that circuit changes with time.

+Worked Examplesi3 questions
  1. Example 6.1Consider Experiment 6.2. (a) What would you do to obtain a large deflection of the galvanometer? (b) How would you demonstrate the presence…Free
  2. Example 6.2A square loop of side $10\ \text{cm}$ and resistance $0.5\ \Omega$ is placed vertically in the east-west plane. A uniform magnetic field of…Preview
  3. Example 6.3A circular coil of radius $10\ \text{cm}$, $500$ turns and resistance $2\ \Omega$ is placed with its plane perpendicular to the horizontal c…Preview
6.5

Lenz's Law and Conservation of Energy

Lenz’s law gives the polarity of the induced emf. It states:

+Worked Examplesi2 questions
  1. Example 6.4Figure 6.7 shows planar loops of different shapes moving out of or into a region of a magnetic field which is directed normal to the plane o…Free
  2. Example 6.5(a) A closed loop is held stationary in the magnetic field between the north and south poles of two permanent magnets held fixed. Can we hop…Preview
6.6

Motional Electromotive Force

When a conductor moves through a uniform, time-independent magnetic field, an emf is induced across it. This is called motional electromotive force.

+Worked Examplesi2 questions
  1. Example 6.6A metallic rod of $1\ \text{m}$ length is rotated with a frequency of $50\ \text{rev/s}$, with one end hinged at the centre and the other en…Free
  2. Example 6.7A wheel with $10$ metallic spokes each $0.5\ \text{m}$ long is rotated with a speed of $120\ \text{rev/min}$ in a plane normal to the horizo…Preview
6.7

Inductance

Whenever a current flows through a coil, it creates a magnetic flux () through that coil (or through a nearby coil).

6.7.1

Mutual Inductance

Mutual inductance is the ability of one coil to induce an electromotive force (emf) in a nearby coil due to a change in its own current. It quantifies the magnetic coupling between two circuits.

+Worked Examplesi1 question
  1. Example 6.8Two concentric circular coils, one of small radius $r_1$ and the other of large radius $r_2$, such that $r_1 \ll r_2$, are placed co-axially…Preview
6.7.2

Self-inductance

Self-inductance is the phenomenon where a changing current in a coil induces an emf in the same coil. This happens because the current produces a magnetic flux through the coil; when the current chang…

+Worked Examplesi1 question
  1. Example 6.9(a) Obtain the expression for the magnetic energy stored in a solenoid in terms of magnetic field $B$, area $A$ and length $l$ of the soleno…Preview
6.8

AC Generator

An AC generator (alternator) converts mechanical energy into electrical energy using electromagnetic induction.

+Worked Examplesi1 question
  1. Example 6.10Kamla peddles a stationary bicycle. The pedals of the bicycle are attached to a $100$ turn coil of area $0.10\ \text{m}^2$. The coil rotates…Preview

Summary

- Magnetic Flux: ; SI unit: weber (Wb). - Faraday’s Law: Induced emf ; magnitude for turns. - Lenz’s Law: Induced current opposes the change in flux; gives the negative sign in Faraday’s law.

Points to Ponder

1. The deep link between electricity and magnetism was uncovered in two stages. First, early 19th-century work by Oersted, Ampère, and others showed that moving charges (an electric current) create a…

Exercises

+Show 8 questions8 questions
  1. 6.1Predict the direction of induced current in the situations described by the following Figs. 6.15(a) to (f). ![Figure 6.15 — six configuratio…Free
  2. 6.2Use Lenz's law to determine the direction of induced current in the situations described by Fig. 6.16: (a) A wire of irregular shape turning…Free
  3. 6.3A long solenoid with $15$ turns per cm has a small loop of area $2.0\ \text{cm}^2$ placed inside the solenoid normal to its axis. If the cur…Free
  4. 6.4A rectangular wire loop of sides $8\ \text{cm}$ and $2\ \text{cm}$ with a small cut is moving out of a region of uniform magnetic field of m…Preview
  5. 6.5A $1.0\ \text{m}$ long metallic rod is rotated with an angular frequency of $400\ \text{rad s}^{-1}$ about an axis normal to the rod passing…Preview
  6. 6.6A horizontal straight wire $10\ \text{m}$ long extending from east to west is falling with a speed of $5.0\ \text{m s}^{-1}$, at right angle…Preview
  7. 6.7Current in a circuit falls from $5.0\ \text{A}$ to $0.0\ \text{A}$ in $0.1\ \text{s}$. If an average emf of $200\ \text{V}$ induced, give an…Preview
  8. 6.8A pair of adjacent coils has a mutual inductance of $1.5\ \text{H}$. If the current in one coil changes from $0$ to $20\ \text{A}$ in $0.5\…Preview

Exemplar Problems

Higher-order thinking / exemplar-style practice problems.

+Show 31 questions31 questions
  1. Q1A square of side $L$ metres lies in the $x$-$y$ plane in a region where the magnetic field is given by $\mathbf{B} = B_0(2\hat{i} + 3\hat{j}…Free
  2. Q2A loop, made of straight edges, has six corners at $A(0,0,0)$, $B(L,0,0)$, $C(L,L,0)$, $D(0,L,0)$, $E(0,L,L)$ and $F(0,0,L)$. A magnetic fie…Free
  3. Q3A cylindrical bar magnet is rotated about its axis. A wire is connected from the axis and is made to touch the cylindrical surface through a…Free
  4. Q4Two circular coils A and B are placed side by side in the same plane a short distance apart, with A on the left and B on the right. Coil A c…Preview
  5. Q5Same as in Problem 4 except that the coil $A$ is made to rotate about a vertical axis. No current flows in $B$ if $A$ is at rest. The curren…Preview
  6. Q6The self inductance $L$ of a solenoid of length $l$ and area of cross-section $A$, with a fixed number of turns $N$, increases as (a) l and…Preview
  7. Q7Consider a magnet surrounded by a wire with an on/off switch $S$. If the switch is thrown from the off position (open circuit) to the on pos…Preview
  8. Q8A wire in the form of a tightly wound solenoid is connected to a DC source, and carries a current. If the coil is stretched so that there ar…Preview
  9. Q9A solenoid is connected to a battery so that a steady current flows through it. If an iron core is inserted into the solenoid, will the curr…Preview
  10. Q10Consider a metal ring kept on top of a fixed solenoid (say on a cardboard). The centre of the ring coincides with the axis of the solenoid.…Preview
  11. Q11Consider a metal ring kept (supported by a cardboard) on top of a fixed solenoid carrying a current $I$. The centre of the ring coincides wi…Preview
  12. Q12Consider a metallic pipe with an inner radius of $1\ \text{cm}$. If a cylindrical bar magnet of radius $0.8\ \text{cm}$ is dropped through t…Preview
  13. Q13A magnetic field in a certain region is given by $\mathbf{B} = B_0 \cos(\omega t)\,\hat{k}$ and a coil of radius $a$ with resistance $R$ is…Preview
  14. Q14Consider a closed loop $C$ in a magnetic field. The flux passing through the loop is defined by choosing a surface whose edge coincides with…Preview
  15. Q15A straight conducting wire PQ slides smoothly, without changing its orientation, over two long straight parallel conducting rails that lie i…Preview
  16. Q16The current i through a solenoid varies with time t along three straight-line segments OA, AB and BC. Starting from the origin O at (t = 0,…Preview
  17. Q17There are two coils $A$ and $B$ separated by some distance. If a current of $2\ \text{A}$ flows through $A$, a magnetic flux of $10^{-2}\ \t…Preview
  18. Q18A magnetic field $\mathbf{B} = B_0 \sin(\omega t)\,\hat{k}$ covers a large region where a wire $AB$ slides smoothly over two parallel conduc…Preview
  19. Q19A conducting wire XY of mass m and negligible resistance can slide smoothly, staying perpendicular to two long parallel horizontal conductin…Preview
  20. Q20ODBAC is a fixed rectangular conducting frame of negligible resistance in which the segment CO is left open (not connected). O is the mid-po…Preview
  21. Q21An infinitely long straight wire lies in the plane of the paper and carries a current I(t) whose rate of change dI/dt = λ is constant. A rec…Preview
  22. Q22A rectangular loop of wire ABCD, of resistance R, lies in the plane of and close to an infinitely long straight wire carrying a current I(t)…Preview
  23. Q23A magnetic field $\mathbf{B}$ is confined to a region $r \le a$ and points out of the paper (the $z$-axis), $r = 0$ being the centre of the…Preview
  24. Q24A rod of mass $m$ and resistance $R$ slides smoothly over two parallel perfectly conducting wires kept sloping at an angle $\theta$ with res…Preview
  25. Q25A straight conducting rod AB of resistance R slides smoothly, remaining perpendicular to two long parallel frictionless conducting rails tha…Preview
  26. Q26A metallic ring of mass $m$ and radius $l$ (ring being horizontal) is falling under gravity in a region having a magnetic field. If $z$ is t…Preview
  27. Q27A long solenoid $S$ has $n$ turns per metre, with diameter $a$. At the centre of this coil, we place a smaller coil of $N$ turns and diamete…Preview
  28. Q28A metal plate is getting heated. It can be because (a) a direct current is passing through the plate. (b) it is placed in a time varying mag…Preview
  29. Q29An emf is produced in a coil, which is not connected to an external voltage source. This can be due to (a) the coil being in a time varying…Preview
  30. Q30The mutual inductance $M_{12}$ of coil 1 with respect to coil 2 (a) increases when they are brought nearer. (b) depends on the current passi…Preview
  31. Q31A circular coil expands radially in a region of magnetic field and no electromotive force is produced in the coil. This can be because (a) t…Preview

Sample & Board Papers

Sample papers and previous-year board questions for this subject.

+Show 1 question1 question
  1. Q1A rectangular frame of wire is placed in a uniform magnetic field directed outwards, normal to the paper. AB is connected to a spring which…Preview