Electromagnetic Induction

Electromagnetic induction is the production of an EMF by a changing magnetic field — the discovery that links electricity and magnetism and powers every generator and transformer. The starting quantity is the magnetic flux through a loop, $\Phi = BA\cos\theta$, where $\theta$ is the angle between the field and the normal to the area. Flux is measured in webers and can change by altering $B$, the area $A$, or the orientation $\theta$.

Faraday's law states that the induced EMF equals the rate of change of flux: $\varepsilon = -\dfrac{d\Phi}{dt}$. For a coil of $N$ turns it becomes $\varepsilon = -N\dfrac{d\Phi}{dt}$. The faster the flux changes, the larger the EMF — so a magnet thrust quickly into a coil induces a bigger EMF than one moved slowly, a standard NEET demonstration.

The minus sign is Lenz's law: the induced current always flows in the direction that opposes the change producing it. Push a north pole towards a coil and the near face becomes a north pole to repel it; pull it away and that face becomes a south pole to attract it. Lenz's law is simply conservation of energy in disguise — you must do work against this opposition, and that work becomes the electrical energy generated.

This opposition has real consequences NEET likes to probe. A magnet dropped through a copper pipe falls slowly because the induced currents oppose its motion, and a generator becomes harder to turn as more current is drawn. Recognising that the induced effect always fights the change is the single most useful habit for solving induction problems quickly and correctly.

An EMF can be induced not only by a changing field but also by motion. When a conducting rod of length $L$ moves with velocity $v$ perpendicular to a field $B$, the free charges in it feel a magnetic force and pile up at the ends, setting up a motional EMF $\varepsilon = BLv$. This is the basic mechanism of a generator, where a coil rotates in a field to produce a continuously varying EMF.

The motional-EMF picture is fully consistent with Faraday's law: as the rod slides along rails, it sweeps out area and changes the flux through the circuit, and $d\Phi/dt = BLv$ gives the same result. If the circuit is closed with resistance $R$, a current $I = \dfrac{BLv}{R}$ flows, and a retarding force $F = BIL$ acts on the rod — again opposing its motion, in line with Lenz's law.

The power delivered shows energy conservation clearly: the mechanical power needed to keep the rod moving, $P = Fv = \dfrac{B^{2}L^{2}v^{2}}{R}$, exactly equals the electrical power dissipated in the resistor. Whoever or whatever pushes the rod does the work that appears as electrical energy — there is no free lunch, a point NEET enjoys testing conceptually.

When changing flux passes through a bulk conductor rather than a thin wire, it drives swirling eddy currents. These cause heating (used in induction stoves and furnaces) and damping (used in galvanometers and electric brakes), but also waste energy in transformer cores. To reduce this loss, cores are laminated — built from thin insulated sheets that break up the eddy-current paths, a practical fact frequently asked in NEET.

A changing current in a coil produces a changing flux through the same coil, inducing an EMF that opposes the change — a phenomenon called self-induction. The coil's self-inductance $L$ links the back-EMF to the rate of change of current: $\varepsilon = -L\dfrac{dI}{dt}$. Inductance is measured in henries and depends only on the coil's geometry and core, just as capacitance depends only on a capacitor's geometry.

For a solenoid, the self-inductance is $L = \mu_0 n^{2} A l$ (with $n$ turns per unit length, area $A$, length $l$), which can be written $L = \dfrac{\mu_0 N^{2} A}{l}$. The key NEET takeaway is that $L \propto N^{2}$ — doubling the turns quadruples the inductance. Inserting an iron core multiplies $L$ by the relative permeability, dramatically increasing it.

An inductor opposes changes in current, so it behaves like electrical inertia: current through it cannot jump instantly. This is why a spark appears when an inductive circuit is switched off — the collapsing current induces a large momentary EMF. It also makes the inductor the time-delaying element in many circuits.

When two coils are placed close together, a changing current in one induces an EMF in the other through their shared flux — mutual induction. The mutual inductance $M$ gives $\varepsilon_2 = -M\dfrac{dI_1}{dt}$, and is the same whichever coil drives the other. Mutual induction is the operating principle of the transformer, tying this topic directly to the next chapter on alternating current.

Building up a current in an inductor requires work against the back-EMF, and this work is stored as energy in the magnetic field. The energy stored is $U = \dfrac{1}{2}LI^{2}$, exactly analogous to the $\tfrac{1}{2}CV^{2}$ of a capacitor but with $L$ in place of $C$ and current in place of voltage. This energy is returned to the circuit when the current decreases.

The energy can also be viewed as residing in the field itself, with an energy density $u = \dfrac{B^{2}}{2\mu_0}$ per unit volume. This mirrors the electric-field energy density $\tfrac{1}{2}\varepsilon_0 E^{2}$ and reinforces the idea that fields, not just charges and currents, carry energy — a unifying theme NEET sometimes draws out.

The most important application of induction is the AC generator (alternator). A coil of $N$ turns and area $A$ rotates with angular frequency $\omega$ in a uniform field $B$, so the flux varies sinusoidally and the induced EMF is $\varepsilon = NBA\omega\sin(\omega t)$. The EMF is therefore alternating, with a peak value $\varepsilon_0 = NBA\omega$ reached when the coil's plane is parallel to the field (flux changing fastest).

This sinusoidal EMF is precisely the alternating voltage analysed in the next chapter. A generator converts mechanical energy (from turbines driven by steam, water or wind) into electrical energy, while a motor does the reverse — the two are essentially the same machine run in opposite directions, a neat symmetry worth remembering for NEET conceptual questions.