Electromagnetic Induction (EMI)

Concept overview

Electromagnetic induction is the phenomenon that a changing magnetic flux induces an EMF in a circuit. Faraday's law quantifies this: EMF = −dΦ_B/dt, where Φ_B = ∫B·dA is the magnetic flux through the circuit. The minus sign is Lenz's law: the induced current opposes the change causing it.

Motional EMF is a special case where a conductor of length L moves at velocity v through a magnetic field B (all mutually perpendicular): EMF = BLv. The charges in the conductor experience a magnetic force F = qv × B that drives them along the wire, creating a potential difference.

Self-inductance L is a property of a circuit — a coil with current I stores magnetic flux Φ = LI. Changing the current induces a back-EMF ε = −L dI/dt that resists the change. For a solenoid of N turns, length ℓ, area A: L = μ₀N²A/ℓ. Mutual inductance M links two coupled coils; the EMF induced in one is M times the rate of current change in the other.

LR circuits show exponential approach to steady-state current, with time constant τ = L/R. Turning a battery on: I(t) = (ε/R)(1 − e^(−t/τ)). Turning it off: I(t) = I₀ e^(−t/τ). Energy stored in an inductor is U = ½LI² — the magnetic analogue of a capacitor's ½CV².

Key formulas & concepts

• Faraday's law: EMF = −dΦ_B / dt
• Motional EMF: EMF = B L v (B, L, v mutually perpendicular)
• Self-inductance: L = μ₀ N² A / ℓ (solenoid); ε = −L dI/dt
• Mutual inductance: M₁₂ = M₂₁; EMF₂ = −M dI₁/dt
• LR time constant: τ = L / R
• LR growth: I(t) = (ε/R)(1 − e^(−t/τ))
• Inductor energy: U = ½ L I²

Common mistakes to avoid

• Forgetting Lenz's law's sign — the induced current must oppose the change in flux, which determines the direction.
• Using B L v when B, L or v are not mutually perpendicular — always resolve into components.
• Confusing L (self) with M (mutual) — both have units of henry but describe different phenomena.
• Ignoring back-EMF when analysing LR circuits — the inductor acts like a battery opposing current change.

JEE Main relevance

JEE Main asks 2 EMI problems every paper — usually one Faraday/motional-EMF and one LR or inductance calculation.

JEE Advanced relevance

Advanced EMI problems combine EMI with mechanics — for instance, a rod sliding down inclined rails with a magnetic field, where induced current gives a retarding force that leads to terminal velocity. LC oscillations also appear at the Advanced level.

Previous-year questions (PYQ)

Motional EMF on inclined rails and mutual-inductance problems dominate the PYQ pool. Drill both.