In 1831, Michael Faraday made one of the most consequential discoveries in the history of science: a changing magnetic field creates an electric current. This phenomenon — electromagnetic induction — is the principle behind every electric generator, every transformer, every induction motor, and every wireless charger in the world. Without Faraday’s discovery, modern electrical civilisation would not exist.
The insight that electricity and magnetism are intimately connected — that you can create one from the other — was revolutionary. Earlier, scientists believed electricity and magnetism were separate phenomena. Faraday showed that a magnet moved through a coil of wire produces current, a current-carrying coil produces a magnetic field that can induce current in a neighbouring coil (mutual induction), and a changing current in a coil produces an EMF within itself (self-induction). James Clerk Maxwell later unified these observations into his famous equations of electromagnetism.
For CBSE Class 12 Physics Chapter 6, electromagnetic induction is a mandatory and high-weightage topic. It includes: magnetic flux, Faraday’s first and second laws, Lenz’s law (with energy conservation), motional EMF, self-induction and inductance (L), mutual induction and mutual inductance (M), eddy currents, the AC generator, and the transformer. This complete guide covers all subtopics with clear explanations, derivations, worked examples, and five CBSE exam-ready FAQs.
The negative sign is from Lenz’s law: induced EMF opposes the cause producing it.
- 1. Magnetic Flux
- 2. Faraday’s Laws of Electromagnetic Induction
- 3. Lenz’s Law and Energy Conservation
- 4. Motional EMF
- 5. Self-Induction and Self-Inductance (L)
- 6. Mutual Induction and Mutual Inductance (M)
- 7. Eddy Currents — Uses and Disadvantages
- 8. AC Generator (Alternator) — Working Principle
- 9. Transformer — Working Principle and Efficiency
- 10. Solved Numerical Problems
- 11. Frequently Asked Questions (FAQ)
1. Magnetic Flux
Magnetic flux (Φ) is a measure of the total magnetic field (B) passing through a given surface area (A). It represents how many magnetic field lines pass through the area.
When B is perpendicular to the surface (parallel to normal): θ = 0°, cosθ = 1 ⇒ Φ = BA (maximum flux)
When B is parallel to the surface (perpendicular to normal): θ = 90°, cosθ = 0 ⇒ Φ = 0 (no flux through surface)
2. Faraday’s Laws of Electromagnetic Induction
Michael Faraday formulated two laws summarising the phenomenon of electromagnetic induction based on his experiments (1831):
The induced EMF exists only as long as the flux is changing. If the flux is constant (even if large), no EMF is induced. The induced EMF drives an induced current if the circuit is closed.
How to change flux: (1) Move a magnet toward/away from a coil. (2) Move the coil in/out of a magnetic field. (3) Rotate the coil in a magnetic field. (4) Change the current in a nearby coil (mutual induction). (5) Change the area of the coil in a field.
e = N × (dΦ/dt) where N = number of turns in the coil and dΦ/dt = rate of change of flux (Wb/s).
Key insight: To get a large induced EMF: (1) Increase N (more turns). (2) Use a stronger magnet (larger B). (3) Move the magnet faster (larger dΦ/dt). (4) Use a larger coil area (larger A, hence larger ΔΦ).
3. Lenz’s Law and Energy Conservation
▼ Lenz’s Law
The negative sign in Faraday’s equation (e = −N dΦ/dt) mathematically represents Lenz’s law — the induced EMF opposes the cause (change in flux).
Example: When a bar magnet’s North pole moves toward a coil, the flux through the coil increases. Lenz’s law says the induced current will create a magnetic field opposing this increase — so the face of the coil nearest the magnet becomes a North pole (repelling the approaching magnet).
When the magnet is pulled away, flux decreases. The induced current now creates a South pole on the nearest face (attracting the retreating magnet, opposing the decrease in flux).
Lenz’s law and energy conservation: The induced current always opposes the motion of the magnet. This means you must do work to move the magnet — the mechanical work done against the opposing force is converted into electrical energy in the coil. Lenz’s law is a consequence of the law of conservation of energy: if induced current aided the cause, it would create energy from nothing (perpetual motion), violating energy conservation.
4. Motional EMF
When a conductor of length L moves with velocity v perpendicular to a magnetic field B, an EMF is induced across the conductor. This is called motional EMF.
Derivation: In time dt, conductor sweeps area dA = L·v·dt. Change in flux: dΦ = B·dA = BLv·dt. EMF = dΦ/dt = BLv
If circuit is closed, induced current I = e/R = BLv/R
Power dissipated = I²R = (BLv)²/R — comes from kinetic energy of moving conductor
5. Self-Induction and Self-Inductance (L)
The induced EMF opposes the change in current (Lenz’s law): if current is increasing, self-induced EMF opposes the increase; if current is decreasing, it opposes the decrease.
Self-inductance (L): L = NΦ/I (Henry, H). It is the ratio of the total flux linkage (NΦ) to the current (I). For a solenoid: L = μ₀N²A/l (where A = cross-section area, l = length, N = number of turns).
Mutual inductance (M): M = N₂Φ₂₁/I₁ (Henry, H). It is the ratio of the flux linkage in the secondary coil (due to primary current) to the primary current. M depends on geometry, number of turns, distance, and medium between coils.
Coupling coefficient: k = M/√(L₁L₂), where 0 ≤ k ≤ 1. k = 1 for perfect coupling (all flux links both coils); k = 0 for no coupling. Transformers aim for k ≈ 1.
6. Eddy Currents — Uses and Disadvantages
When a solid conductor (metal plate or block) moves through a magnetic field, or is placed in a changing magnetic field, circulating currents are induced within the conductor itself. These are called eddy currents (or Foucault currents). They form closed loops perpendicular to the magnetic flux.
| Aspect | Details |
|---|---|
| Cause | Changing magnetic flux through a solid conducting body (by Faraday’s law). Eddy currents oppose the change (by Lenz’s law). |
| Direction | Circulating (swirling) currents within the conductor, opposing the change in flux. |
| Effect | Generate heat (I²R) — waste energy; also create retarding forces on moving conductors. |
| Uses (+) | Electromagnetic braking (trains, roller coasters) • Induction furnaces (melting metals) • Speedometers • Dead-beat galvanometers • Electromagnetic damping • Metal detectors • Induction cooktops • Induction heating |
| Disadvantages (−) | Energy loss in transformer cores (iron loss) • Heating of motor armatures • Heating of transformer cores |
| How to reduce | Use laminated cores (thin insulated sheets of iron instead of solid iron) in transformers and motors. Laminations break the eddy current paths, drastically reducing eddy current magnitude. |
8. AC Generator (Alternator) — Working Principle
An AC generator (alternator) converts mechanical energy into electrical energy using the principle of electromagnetic induction (Faraday’s law).
⚡ AC Generator — Parts and Working
Parts of AC Generator:
- Armature coil: Rectangular coil of N turns (area A) that rotates in the magnetic field. Usually wound on a soft iron core.
- Field magnets: Permanent magnets or electromagnets providing a uniform magnetic field B between the poles.
- Slip rings: Two metal rings connected to the two ends of the armature coil. They rotate with the coil and allow the induced current to flow to the external circuit.
- Carbon brushes: Stationary contacts pressing against the slip rings. They transfer current from the rotating coil to the stationary external circuit.
where e₀ = NBAw = peak EMF, w = angular frequency = 2πf, N = turns, B = field, A = coil area. The output is sinusoidal alternating current (AC).
Why AC, not DC? With slip rings, the connection to the external circuit does not change as the coil rotates — so the output reverses direction every half-turn, giving AC. DC generators use a split-ring commutator to rectify the output to unidirectional DC.
9. Transformer — Working Principle and Efficiency
A transformer transfers electrical energy from one circuit to another (usually at a different voltage) using the principle of mutual induction. It works only on AC (alternating current), not DC.
⚡ Transformer — Construction and Working
Iᴅ = primary current, Iᵀ = secondary current
Step-up transformer: Nᵀ > Nᴅ ⇒ Vᵀ > Vᴅ (increases voltage, decreases current)
Step-down transformer: Nᵀ < Nᴅ ⇒ Vᵀ < Vᴅ (decreases voltage, increases current)
Ideal transformer efficiency: Input power = Output power ⇒ VᴅIᴅ = VᵀIᵀ ⇒ 100% efficiency
Real efficiency: η = (VᵀIᵀ)/(VᴅIᴅ) × 100% (less than 100% due to copper losses + eddy current losses + hysteresis losses)
Why laminated core? To reduce eddy currents (energy loss). Laminated iron cores have thin insulated layers that break up eddy current loops, drastically reducing heat generation.
Power transmission application: Power plants generate electricity at ~11,000 V. Step-up transformers raise this to 220,000–400,000 V for long-distance transmission (high voltage = low current = low I²R losses in cables). Step-down transformers at substations and homes reduce it to 230 V for safe domestic use.
10. Solved Numerical Problems
Induced EMF: |e| = N |dΦ/dt| = 200 × |−0.03/0.5| = 200 × 0.06
Secondary voltage: Vᵀ = Vᴅ × (Nᵀ/Nᴅ) = 220 × 5 = 1100 V (Step-up transformer)
For ideal transformer: VᴅIᴅ = VᵀIᵀ
Iᵀ = VᴅIᴅ/Vᵀ = (220 × 5)/1100 = 1100/1100
Applications of Electromagnetic Induction
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11. Frequently Asked Questions (FAQ)
Faraday’s First Law: Whenever the magnetic flux linked with a circuit changes, an electromotive force (EMF) is induced in the circuit. The induced EMF lasts only as long as the flux is changing.
Faraday’s Second Law: The magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux linked with the circuit.
Mathematical form: |e| = N |dΦ/dt|
Including Lenz’s law (direction): e = −N dΦ/dt
where N = number of turns, dΦ/dt = rate of change of flux per turn, e = induced EMF in Volts.
Lenz’s Law: The direction of the induced EMF (and induced current in a closed circuit) is always such that it tends to oppose the change in magnetic flux that caused it.
Consistency with energy conservation: By Lenz’s law, the induced current creates a magnetic field that opposes the cause (e.g., opposes the motion of a magnet). This means an external agent must do work against this opposing force to maintain the motion. This mechanical work is the source of the electrical energy generated in the coil. If the induced current instead aided the motion (violated Lenz’s law), it would accelerate the magnet, increasing flux, increasing current, accelerating the magnet further — creating energy from nothing (perpetual motion), which violates the law of conservation of energy. So Lenz’s law is a direct consequence of energy conservation.
Self-inductance (L) is the property of a coil by which it opposes any change in the current flowing through it. When the current in a coil changes, the changing flux induces an EMF in the same coil (self-induced EMF): e = −L dI/dt. The self-inductance L is measured in Henry (H). It is defined as L = NΦ/I (ratio of total flux linkage to current).
Factors affecting self-inductance:
(1) Number of turns (N): L ∝ N² (more turns = much greater L)
(2) Cross-sectional area (A): L ∝ A (larger area = greater L)
(3) Length of solenoid (l): L ∝ 1/l (shorter solenoid = greater L)
(4) Permeability of core material (μ): L ∝ μ (iron core gives much larger L than air core)
For a solenoid: L = μ₀μᵅN²A/l
A transformer works on the principle of mutual induction. The primary coil carries an alternating current (AC) that creates a continuously changing magnetic flux in the iron core. This changing flux links with the secondary coil (via the iron core), inducing an alternating EMF in it (by Faraday’s second law). The ratio of secondary to primary voltage equals the turns ratio: Vᵀ/Vᴅ = Nᵀ/Nᴅ.
Why DC doesn’t work: Direct current (DC) is constant (steady). A constant current produces a constant (unchanging) magnetic flux in the primary coil. Since dΦ/dt = 0 for steady DC, Faraday’s law gives e = −N dΦ/dt = 0. No EMF is induced in the secondary coil. A transformer needs changing flux (AC) to function. Applying DC to a transformer also risks burning the primary coil due to very low DC resistance (no back-EMF from self-induction to limit current).
Eddy currents are circulating currents induced in a solid conducting body (metal block or plate) when the magnetic flux through it changes. They are induced by Faraday’s law and directed to oppose the change in flux (Lenz’s law). They flow in closed loops perpendicular to the magnetic field, generating heat (I²R).
Useful applications:
(1) Electromagnetic braking: Eddy currents in train wheel discs create retarding forces when passing through a magnetic field, providing smooth, contactless braking in high-speed trains (no mechanical wear).
(2) Induction furnaces: High-frequency alternating magnetic fields induce powerful eddy currents in metals, heating them to melting temperatures for smelting and metal refining without contact.
Disadvantages:
(1) Energy loss as heat in transformer cores and motor armatures (iron loss), reducing efficiency.
(2) Undesired heating of conducting parts in AC machinery, requiring cooling systems.
Reduction: Laminated cores (thin insulated iron sheets) are used in transformers and motors to break up eddy current loops and reduce their magnitude significantly.
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