Electromagnetic Induction — NEET Notes

The experiments of Faraday and Henry

Throughout the 1820s, Oersted, Ampère and their contemporaries had established that an electric current produces a magnetic field. The opposite question — can a magnetic field produce a current? — was answered by Faraday and Henry in three classic experiments that every NEET student should be able to describe in their sleep. In the first experiment, Faraday pushed the north pole of a bar magnet toward a closed coil connected to a galvanometer. The galvanometer needle deflected. Withdrawing the magnet reversed the deflection. Holding the magnet still produced nothing. The needle's deflection scaled with the speed of motion, confirming that relative motion between magnet and coil — not the field itself — is what matters.

In the second experiment, the bar magnet was replaced by a second coil carrying a steady current from a battery. Moving this current-carrying coil toward or away from the test coil produced the same effect — a current was induced. The result was clean: a current-carrying coil behaves exactly like a magnet, and what matters is still the relative motion. The third experiment went further. Faraday held both coils stationary, but introduced a tapping key in the primary circuit. Pressing the key sent a brief deflection through the galvanometer. Releasing the key produced a deflection in the opposite direction. While the key remained pressed steadily, the galvanometer read zero. Relative motion is therefore not essential — what is essential is that the magnetic flux through the test coil changes. Inserting a soft-iron rod through both coils amplified the effect dramatically by increasing the magnetic field. From these observations Faraday distilled a single unifying idea: a time-varying magnetic flux induces an EMF.

"What is the use of a new born baby?"

Faraday, when asked the use of electromagnetic induction

Magnetic flux

Before stating Faraday's law, we need a precise measure of "how much magnetic field passes through a loop." That measure is the magnetic flux, Φ_B. For a plane of area A in a uniform magnetic field B, the flux is the dot product of the field vector and the area vector:

Φ_B  =  B·A  =  B A cos θ

Magnetic flux through a plane surface in a uniform field

Here θ is the angle between B and the area vector A (perpendicular to the loop). When the field is non-uniform or the surface is curved, the flux generalises to the surface integral Φ_B = ∫B·dA, summing infinitesimal contributions over the whole surface. Flux is a scalar and its SI unit is the weber (Wb), equal to one tesla-metre-squared (T·m²). Three geometric levers can change Φ_B — alter the field magnitude B, change the loop's area A, or rotate the loop so θ changes. Faraday's three experiments correspond to the first lever (changing B); the motional-EMF setup corresponds to the second; the AC generator corresponds to the third.

Faraday's law of induction

Faraday's law converts the experimental observation into a single equation. The induced EMF in a closed loop equals the negative of the rate of change of magnetic flux through the loop. For a single loop:

For a closely wound coil of N turns, each turn links the same flux Φ_B, and each turn contributes an EMF. The total induced EMF therefore picks up a factor of N:

ε  =  − N (dΦ_B/dt)

Faraday's law for an N-turn coil

The quantity NΦ_B is called the flux linkage of the coil. If the coil is part of a closed circuit of resistance R, an induced current I = ε/R flows. The induced EMF is therefore the workhorse: it converts a changing magnetic field into electrical work. Every generator, every transformer, every wireless charging pad operates on this single equation.

Lenz's law and the conservation of energy

In 1834 the German physicist Heinrich Lenz formulated the rule that gives the negative sign its physical meaning. Lenz's law states: the polarity of the induced EMF is such that it tends to produce a current which opposes the change in magnetic flux that produced it. When you push a north pole toward a coil, the coil responds by inducing a current whose own magnetic moment points north toward the approaching magnet — repelling it. When you pull the magnet away, the induced current reverses, presenting a south face toward the receding north pole — attracting it, trying to keep the flux from decreasing. In every case, the induced current resists the change.

This is not a separate empirical law — it is energy conservation in disguise. If the induced current ever aided the flux change, a gentle nudge on a magnet near a coil would launch it into a self-accelerating loop, with kinetic energy appearing from nowhere. Lenz's law forbids this perpetuum mobile. To increase the flux through a coil, you must do mechanical work against the opposing magnetic force; that work is delivered to the circuit and dissipated as Joule heat. Lenz's law is the bookkeeping rule that keeps energy from being created.

The same three-step machine handles every NEET figure, however complicated. The next factor-grid runs the procedure through five canonical scenarios that account for the bulk of asked questions.

Motional EMF — a rod in a magnetic field

Consider a straight conductor PQ of length l sliding along two parallel rails, fully immersed in a uniform magnetic field B perpendicular to the plane of the rails. As the rod moves leftward with velocity v, it sweeps out new area at the rate lv per second. The flux through the rectangular circuit changes accordingly, and Faraday's law gives the induced EMF:

ε  =  − dΦ_B/dt  =  Blv

Motional EMF — rod of length l, velocity v, in field B

The same expression can be derived without invoking Faraday — purely from the Lorentz force. Every free electron in the rod moves with velocity v alongside the rod itself; the magnetic part of the Lorentz force on each electron is qv×B, which pushes positive charge along the rod from one end to the other. The work done in carrying unit charge from one end to the other is vBl, which by definition is the EMF. Both pictures — the flux-rule picture and the Lorentz-force picture — give ε = Blv. NCERT explicitly highlights this dual derivation as Faraday's deep insight: moving charges in a static field and static charges in a time-varying field are two faces of the same symmetric phenomenon, a hint at the relativity that Einstein would later make explicit.

A common variant — and a NEET favourite — replaces translation with rotation. A conducting rod of length l rotated about one end with angular velocity ω in a perpendicular field B develops an EMF between its ends of ε = ½ Bωl². Each element dr at distance r from the pivot has speed ωr and contributes B(ωr)dr; integrating from 0 to l gives the half-Bωl² result.

Induced EMF in a rotating coil & the AC generator

The third lever — rotating a coil so that θ between A and B changes — is the operating principle of every commercial generator. Consider an N-turn coil of area A rotated with constant angular velocity ω in a uniform field B. Setting θ = ωt (so the coil's area vector is parallel to B at t = 0), the flux at time t is

Φ_B  =  B A cos ωt

Flux through a coil rotating at angular velocity ω

Differentiating, the induced EMF is

ε  =  −N dΦ_B/dt  =  N B A ω sin ωt

EMF of an N-turn coil rotating in a uniform field

The instantaneous EMF varies sinusoidally between +ε₀ and −ε₀, where the peak EMF ε₀ = N B A ω. The polarity reverses every half-cycle — hence alternating current. The frequency of rotation in India is 50 Hz; in the United States, 60 Hz. NEET 2022 (Q.38) tested this directly: a 1000-turn coil, radius 10 m, rotating at 2 rad/s in 2 × 10⁻⁵ T gave a maximum current of 1 A through a 12.56 Ω resistance — confirming i_max = NBAω/R. A practical AC generator uses an armature (the rotating coil) connected via slip rings and brushes to the external circuit; in commercial units the coils are often held stationary while the electromagnets rotate — mechanically simpler at high power.

Self-induction & energy stored in an inductor

When the current through a coil changes, the magnetic flux it produces through itself also changes — and by Faraday's law this changing self-flux induces an EMF in the very same coil that opposes the current change. The phenomenon is called self-induction. Because the flux through the coil is proportional to its own current, we write Φ_B = (L/N)·I per turn, so the flux linkage is

N Φ_B  =  L I

Flux linkage of a coil of self-inductance L carrying current I

The constant of proportionality L is the self-inductance, measured in henries (H) in honour of Joseph Henry. Combining with Faraday's law:

For a long solenoid of n turns per unit length, length l, and cross-sectional area A, the magnetic field inside is B = μ₀nI; the flux linkage works out to Nμ₀nl·A·I, leading to the canonical formula:

Because work has to be done against the back-EMF to establish a current in an inductor, energy is stored in the coil's magnetic field. At any instant, the rate of work done by the source is εI = LI(dI/dt). Integrating from zero up to final current I gives the energy stored in an inductor:

U  =  ½ L I²

Magnetic energy stored in an inductor

This is the magnetic analogue of ½mv² in mechanics — confirming the inertia interpretation of L. NCERT also expresses the energy per unit volume of the magnetic field as u_B = B²/(2μ₀), valid for any region containing a magnetic field. NEET 2023 (Q.23) and NEET 2018 (Q.3) both tested U = ½LI² directly — these are guaranteed marks if the formula is memorised.

Mutual induction — coils that talk to each other

If a second coil sits near the first, the flux produced by the first coil's current also threads the second. When that flux changes, an EMF is induced in the second coil. This phenomenon — flux from one coil inducing EMF in another — is called mutual induction. The flux linkage through coil 1 due to current I₂ in coil 2 is N₁Φ₁ = M₁₂I₂, where M₁₂ is the mutual inductance of coil 1 with respect to coil 2. Differentiating:

ε₁  =  −M (dI₂/dt)

EMF induced in coil 1 by changing current in coil 2

NCERT proves an important reciprocity theorem: M₁₂ = M₂₁ = M. The flux coil 1 links from coil 2's current equals the flux coil 2 links from the same current in coil 1. For two long coaxial solenoids of length l, with n₁ and n₂ turns per unit length and the inner solenoid of radius r₁, the mutual inductance is M = μ₀n₁n₂πr₁²l. NEET 2021 (Q.40) tested mutual inductance for two concentric circular loops of radii R₁ and R₂ with R₁ ≫ R₂: the answer M ∝ R₂²/R₁ follows from approximating the inner loop as immersed in the uniform central field of the outer loop. Mutual inductance is the principle behind transformers, wireless charging pads, RFID readers, and induction cooktops.

Eddy currents (Foucault currents) & applications

So far we have considered induced currents in coiled wires. But Faraday's law applies to any conductor — including a solid block of metal. When the flux through a bulk conductor changes, induced currents circulate in closed loops within the body of the conductor itself. These swirling currents — discovered by Léon Foucault in 1855 — are called eddy currents. They dissipate energy as heat through the conductor's resistance, and they exert forces that resist the cause of the flux change.

NIOS supplements NCERT on this topic with explicit applications. The retarding force of eddy currents is exploited in electromagnetic brakes: a metal disc rotating in a magnetic field decelerates because the induced eddy currents oppose its motion. The high-speed trains, modern roller coasters, and the moving-coil galvanometer's damping all rely on this. The dissipation itself — turning electromagnetic energy into heat — is the basis of induction furnaces, where high-frequency alternating fields heat a metal sample to its melting point without any contact. Induction cooktops work similarly: the coil under the glass top generates an alternating magnetic field that induces eddy currents in a ferromagnetic pan, heating the pan directly while the glass stays cool. Speedometers on older cars used an aluminium drum dragged by a rotating magnet through eddy-current torque.

The same effect is a nuisance in transformers and electric-motor cores, where eddy currents waste energy and heat the iron. The standard fix is to laminate the core — assemble it from thin insulated sheets of iron rather than a solid block — which interrupts the eddy-current loops and slashes the I²R losses. NEET-pattern questions sometimes ask "why are transformer cores laminated?" — the answer is always: to reduce eddy-current losses.