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Physics · Class 12 Science

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

For more than half a century after Hans Christian Oersted showed in 1820 that an electric current produces a magnetic field, physicists wondered whether the reverse effect might also be true -- could a magnetic field somehow produce an electric current? Michael Faraday in England and Joseph Henry in America, working in…

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Key concepts

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Faraday's Law of Electromagnetic Induction

Faraday's laws state that a changing magnetic flux linked with a closed circuit induces an emf in it, with magnitude , or, including Lenz's law's direction as a minus sign, .

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In previous exams

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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 more than half a century after Hans Christian Oersted showed in 1820 that an electric current produces a magnetic field, physicists wondered whether the reverse effect might also be true -- could…

6.2

Magnetic Flux

Defining magnetic flux. Just as the flow of water through a net can be measured by how much water crosses it per second, the 'amount' of a magnetic field passing through a given surface is measured by…

6.3

Faraday's Laws of Electromagnetic Induction

Faraday's first law (qualitative). Whenever the magnetic flux linked with a closed circuit changes, an emf is induced in the circuit; this induced emf lasts only as long as the flux keeps changing, an…

6.4

Induced EMF and Induced Current

Faraday's law says an emf is induced whenever the flux linkage changes, but since depends on THREE separate quantities -- the field , the area , and the angle -- flux can change because any one (or mo…

6.5

Lenz's Law and Conservation of Energy

Statement of Lenz's law. Faraday's law gives the magnitude of the induced emf but is silent, on its own, about which way the induced current flows. Heinrich Lenz supplied the missing rule in 1834:

6.6

Eddy Currents

What an eddy current is. Faraday's law does not care whether the changing flux threads through a neat, thin wire loop or through a solid block of conducting metal -- either way, changing flux induces…

6.7

Self and Mutual Inductance: General Concepts

The core idea shared by both. A changing current in ANY coil sets up a changing magnetic field, and hence a changing flux, in the space around it.

6.7.1

Self-Inductance of a Solenoid

Setting up the solenoid. Consider a long solenoid of length , cross-sectional area , wound with a total of turns, so that it has turns per unit length.

6.7.2

Mutual Inductance of Two Coaxial Solenoids

The geometry. Consider two long solenoids of the SAME length , wound coaxially -- one directly inside the other, sharing a common central axis, as shown in the figure for this section.

6.8

Energy Stored in an Inductor

Why establishing a current costs energy. As a current in an inductor is being built up from zero, the self-induced back emf (Section 6.7) continuously opposes the increase, so whatever source is drivi…

Summary

Magnetic flux through a flat surface of area in a uniform field is (SI unit weber, Wb), maximum when the surface is perpendicular to and zero when it is parallel to ; for an -turn coil the total flux…

Sample & Board Papers

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

+Show 14 questions14 questions
  1. Q1a) State Faraday's laws of electromagnetic induction. b) The magnetic flux through a coil is varying according to the relation φ = (4t² + 2t…Preview
  2. Q2a) State Lenz's law related to the electromagnetic induction. b) What is eddy current? c) What is meant by 'self-inductance of a coil is 1 H…Preview
  3. Q3Derive an expression for the coefficient of self-inductance of a long air-cored solenoid of length l and number of turns N. **OR** A coil of…Preview
  4. Q4When the current in a coil changes from +10A to −10A in 0.08s an emf of 50 V is induced. The coefficient of self-induction of the coil is (a…Preview
  5. Q5Write the relation between weber and tesla units.Preview
  6. Q6(a) Define self-inductance of a coil. Show that magnetic energy required to build up the current I in a coil of self-inductance L is given b…Preview
  7. Q7When a magnet is taken towards a coil, the induced emf depends on (a) the number of turns in the coil (b) the speed of the magnet (c) the re…Preview
  8. Q8Why is spark produced in the switch of an electric circuit, when light is put off?Preview
  9. Q9When a current changes from +2A to –2A in 0.05 second, an emf of 8 volt is induced in a coil. The coefficient of self-induction (L) of the c…Preview
  10. Q10Which principle is obeyed by Lenz's law?Preview
  11. Q11(a) State Faraday's laws of electromagnetic induction. (b) The magnetic flux through a coil is varying according to the relation φ = (4t² +…Preview
  12. Q12The dimensional formula of coefficient of mutual inductance is (a) [ ML²T⁻²I² ] (b) [ ML²T⁻²I⁻² ] (c) [ ML⁻²T²I² ] (d) [ ML⁻²T⁻²I⁻² ]Preview
  13. Q13A square loop of side 1 m and resistance 1 Ω is placed in a magnetic field of 0·5 T. If the plane of loop is perpendicular to the direction…Preview
  14. Q14The expression for the magnetic flux in a circuit having resistance 7 Ω is φ = 6t² − 5t + 4. In time t = 1 second, the induced current will…Preview

More questions

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+Show 8 questions8 questions
  1. Example 1State Faraday's laws of electromagnetic induction, both in words and as the single mathematical statement $\mathcal{E}=-N\dfrac{d\Phi_B}{dt}…Free
  2. Example 2Define magnetic flux through a plane surface placed in a uniform magnetic field. Write its formula, name its SI unit, and state the two situ…Free
  3. Example 3State Lenz's law. Explain, with the help of the negative sign in Faraday's law, what the law tells us about the direction of an induced curr…Free
  4. Example 4Using the example of a bar magnet's north pole being pushed into a closed coil, explain why Lenz's law is a direct consequence of the law of…Preview
  5. Example 5What are eddy currents? Explain, with a reason, why the iron core of a transformer is built up of thin, mutually insulated laminations inste…Preview
  6. Example 6Name and briefly describe two everyday devices or techniques that make deliberate use of eddy currents.Preview
  7. Example 7Define the coefficient of self-inductance of a coil. Starting from the relation $N\Phi_B=LI$, derive the expression for the emf self-induced…Preview
  8. Example 8Define mutual inductance between two coils. State the reciprocity relation connecting $M_{12}$ and $M_{21}$, and explain in words what it me…Preview
+Show 9 questions9 questions
  1. Q9A straight conducting rod of length $l$ slides with a uniform velocity $v$ along two parallel rails, in a region of uniform magnetic field $…Free
  2. Q10A plane loop of area $A$ is placed in a uniform magnetic field $B$ such that the normal to the loop makes an angle $\theta$ with $B$. Write…Free
  3. Q11A bar magnet is moved with its north pole leading towards a stationary closed circular coil, along the coil's axis. Using Lenz's law, find t…Free
  4. Q12A thick sheet of copper is allowed to swing like a pendulum between the pole pieces of a strong magnet. Explain why it comes to rest after o…Preview
  5. Q13A long solenoid has $N$ turns wound uniformly over a length $l$, with $n=N/l$ turns per unit length and cross-sectional area $A$. Derive the…Preview
  6. Q14Two long solenoids of the same length $l$ are wound coaxially, one inside the other, with the inner solenoid of radius $r_1$ having $n_1$ tu…Preview
  7. Q15A rectangular conducting loop is being pulled at a constant velocity out of a region of uniform magnetic field, through the field's boundary…Preview
  8. Q16Apart from physically moving a coil or a magnet, state two other ways in which the magnetic flux linked with a stationary coil can be change…Preview
  9. Q17Show that the henry, the SI unit of self- and mutual inductance, can be written equivalently as volt-second-per-ampere (V s A$^{-1}$) and as…Preview
+Show 7 questions7 questions
  1. Q18A circular coil of 50 turns and area $0.20\ \text{m}^2$ is placed with its plane perpendicular to a uniform magnetic field of $0.4\ \text{T}…Free
  2. Q19The magnetic flux through each turn of a coil of 100 turns changes from $2\times10^{-3}\ \text{Wb}$ to $8\times10^{-3}\ \text{Wb}$ in $0.2\…Free
  3. Q20A straight conducting rod of length $0.5\ \text{m}$ moves with a speed of $4\ \text{m/s}$, perpendicular both to its own length and to a uni…Free
  4. Q21A square conducting loop of side $10\ \text{cm}$ lies with its plane perpendicular to a uniform magnetic field of $0.5\ \text{T}$. The loop…Preview
  5. Q22A long solenoid has 2000 turns wound over a length of $1\ \text{m}$, with a cross-sectional area of $4\times10^{-3}\ \text{m}^2$. (a) Calcul…Preview
  6. Q23Two long coaxial solenoids, each of length $0.5\ \text{m}$, are wound one inside the other: the inner solenoid has radius $2\ \text{cm}$ and…Preview
  7. Q24A coil of self-inductance $2\ \text{H}$ carries a steady current of $5\ \text{A}$. Calculate the energy stored in its magnetic field.Preview