Electromagnetic Induction: Faraday's Law, Lenz's Law & Inductance
Study how changing magnetic flux induces EMF, learn Faraday's law, Lenz's law, motional EMF, self and mutual inductance, AC generator and transformer for JEE Main Physics.
The central idea of this chapter
Changing magnetic flux through a circuit induces an EMF. This chapter connects magnetic field, flux, induced current and energy through Faraday's law, Lenz's law and inductance.
What should you understand first?
Electromagnetic induction is the basis of generators, transformers and many electrical devices. Once you understand flux, induced EMF and direction rules, most problems become systematic applications.
Core concepts
- Magnetic flux Φ = B·A
- Faraday's law ε = −dΦ/dt
- Lenz's law Opposes change
- Motional EMF ε = Blv
- Self & mutual inductance L, M
Useful building blocks
- Straight conductor ε = Blv sinθ
- Rotating rod ε = ½Bωl²
- Solenoid L = μ₀N²A/l
- Transformer Vs/Vp = Ns/Np
- Energy in inductor U = ½LI²
Electromagnetic Induction formula sheet
Use flux definition and sign conventions consistently. Apply Lenz's law to find direction before using magnitude formulas.
| Topic | Formula / Relation | Meaning or use |
|---|---|---|
| Magnetic flux | Φ = B·A = BA cosθ | Total magnetic field through area A |
| Faraday's law | ε = −N dΦ/dt | Induced EMF in coil of N turns |
| Lenz's law | Direction opposes change in Φ | Determines polarity of induced EMF |
| Motional EMF (straight) | ε = Blv sinθ | Conductor of length l moving in B with velocity v |
| Motional EMF (rotating rod) | ε = ½Bωl² | Rod of length l rotating with angular speed ω |
| Self inductance | L = NΦ/I | Flux linkage per unit current |
| Solenoid inductance | L = μ₀N²A/l | N turns, area A, length l |
| Mutual inductance | M = N₂Φ₂₁/I₁ | Flux in coil 2 due to current in coil 1 |
| Induced EMF in inductor | ε = −L dI/dt | Self-induced EMF due to changing current |
| Energy in inductor | U = ½LI² | Energy stored in magnetic field |
| Transformer ratio | Vs/Vp = Ns/Np | Ideal transformer, s = secondary, p = primary |
| AC generator EMF | ε = NBAω sinωt | Coil of N turns, area A, rotating in B with ω |
How to approach EMI problems
First find how flux is changing (B, A or θ), then apply Faraday's law. Use Lenz's law for direction and inductance formulas for coils and circuits.
Induced EMF
- Moving conductor? ε = Blv
- Changing area? dΦ/dt via A
- Changing field? dΦ/dt via B
- Rotating coil? ε = NBAω sinωt
- Direction? Use Lenz's law
Inductance & circuits
- Self inductance? L = NΦ/I
- Mutual inductance? M = N₂Φ₂₁/I₁
- Energy stored? U = ½LI²
- Transformer? V ratio = N ratio
- LR circuit? τ = L/R
How to prepare Electromagnetic Induction
Start with magnetic flux and Faraday's law, then learn motional EMF and inductance. Finish with AC generator, transformer and LR circuit basics.
What to do
- Learn flux definition and Faraday's law with Lenz's law
- Practise motional EMF for straight and rotating conductors
- Master self and mutual inductance formulas for solenoid and coils
- Understand AC generator principle and transformer ratio
- Revise energy in inductor and basic LR circuit ideas
Common mistakes
- Forgetting negative sign in Faraday's law (Lenz's law)
- Using wrong angle in flux formula (θ between B and area vector)
- Confusing self inductance and mutual inductance formulas
- Not checking whether transformer is step-up or step-down
- Ignoring conditions for ideal transformer in problems
Ready to test Electromagnetic Induction?
Revise the formula sheet, then solve mixed JEE Main problems on induced EMF, inductance and AC devices.
Electromagnetic Induction FAQ
Short answers to frequently tested ideas in this chapter.
Faraday's law states that the induced EMF in a closed loop equals the negative rate of change of magnetic flux through the loop. It is written as ε = −dΦ/dt.
Lenz's law states that the direction of induced current is such that it opposes the change in magnetic flux that produced it. This is represented by the negative sign in Faraday's law.
Self inductance is the property of a coil by which it opposes any change in current flowing through it. It is defined as L = NΦ/I, where N is number of turns and Φ is magnetic flux.