Electromagnetic induction is the phenomenon in which a changing magnetic flux through a circuit produces an electromotive force (emf) — and hence a current, if the circuit is closed. It is the single idea behind generators, transformers, inductors, and the entire AC power grid.
The Central Discovery
Michael Faraday found (1831) that a current is induced in a coil not when a magnet sits still near it, but only while the magnet moves — that is, only while the magnetic flux linked with the coil is changing. A steady magnet, however strong, induces nothing.
Magnetic Flux
The key quantity is magnetic flux ΦB through a surface of area A in a field B:
ΦB=B⋅A=BAcosθ
where θ is the angle between B and the area's normal. Its SI unit is the weber (Wb), where 1Wb=1T⋅m2.
Flux can change in three distinct ways, and any of them induces an emf:
the field strength B changes,
the area A of the loop changes,
the orientation θ changes (a coil rotating in a field — the basis of the generator).
Faraday's Law
The induced emf equals the negative rate of change of flux. For a coil of N turns:
E=−NdtdΦB
The faster the flux changes, the larger the emf. This is why a magnet dropped quickly through a coil gives a bigger deflection than one moved slowly.
Lenz's Law — the Minus Sign
The negative sign expresses Lenz's law: the induced current flows in the direction that opposes the change producing it. Push a magnet's north pole toward a coil, and the coil's near face becomes a north pole to repel it; pull it away, and the face becomes a south pole to attract it. This is simply energy conservation — you must do work against this opposition, and that work becomes the electrical energy of the induced current.
Motional emf
A special, very useful case: a conducting rod of length l moving with speed v perpendicular to a field B sweeps out area and develops an emf
E=Blv
Here the emf arises because the free charges in the rod experience a magnetic force qv×B, which drives them along the rod.
Note
Induction does not require physical contact or a battery. It is the change of flux that matters, not its value. A loop sitting in a huge but constant field has zero induced emf.
Where It Leads
Once a coil's own changing current induces an emf in itself, we call it self-inductance (L); when one coil's changing current induces emf in a neighbour, that is mutual inductance (M). Both are direct consequences of Faraday's law. Rotate a coil steadily in a magnetic field and the sinusoidal emf it produces is exactly the alternating voltage that runs the AC circuits studied in this chapter.
Faraday's and Lenz's laws of electromagnetic induction form one of the highest-weightage chapters in NCERT Class 12 Physics, tested extensively in CBSE boards, JEE Main and NEET. Anyone searching "Faraday's law of electromagnetic induction formula and examples class 12 physics" will find this changing-flux explanation, including the motional emf case, is exactly how NCERT presents the chapter.
Why this formula?
Electromagnetic Induction
Electromagnetic induction is the effect discovered by Faraday: a changing magnetic flux through a circuit drives an induced EMF (and hence a current). The key word is changing — a steady field, however strong, induces nothing.
Magnetic flux
Flux measures how many field lines thread a surface bounded by the loop:
ΦB=∫B⋅dA=BAcosθ
It can change three ways: by changing B, by changing the area A, or by rotating the loop (changing θ).
Faraday's law
The induced EMF equals the rate of change of flux:
E=−dtdΦB
For a coil of N turns, E=−NdtdΦB. The EMF depends on how fast the flux changes, not on the flux itself — a slow change gives a small EMF, a rapid change a large one.
Lenz's law — the minus sign
The negative sign is Lenz's law: the induced current flows in the direction that opposes the change producing it. Push a magnet's north pole toward a coil and the coil's near face becomes a north pole to repel it; pull it away and the face becomes a south pole to attract it. This opposition is required by energy conservation — you must do work against the induced current, and that work is what becomes electrical energy. If the current instead aided the change, energy would be created from nothing.
A worked idea
A rod of length l slides at speed v along rails in a field B. In time dt it sweeps area lvdt, so the flux changes by dΦB=Blvdt, giving a motional EMF:
E=dtdΦB=Blv
The same result follows from the magnetic force q(v×B) pushing free electrons to one end of the rod — a direct check that Faraday's law and the Lorentz force tell one consistent story.
First law: changing flux induces an emf. Second law: the induced emf's magnitude equals the rate of change of flux linkage.
✓Final answer
First law: whenever flux linked with a closed circuit changes, an emf is induced. Second law: the induced emf equals −d(NΦB)/dt.
Step 1. First law: whenever the magnetic flux linked with a closed circuit changes, an emf is induced in the circuit, lasting exactly as long as the flux keeps changing.
Step 2. Second law: the magnitude of the induced emf in a closed circuit is equal to the time rate of change of the magnetic flux linked with the circuit.
Step 3. For a coil of N turns, combining the second law with Lenz's law gives ε=−dtd(NΦB), where NΦB is the flux linkage.
✓Final answer
First law: a changing flux linked with a closed circuit induces an emf. Second law: the induced emf's magnitude equals the time rate of change of the flux linkage, ε=−d(NΦB)/dt.
State both of Faraday's laws in their standard form, including the flux-linkage emf formula.
Stating only one of the two laws when both are asked for.
Omitting the number of turns N (flux linkage) for a multi-turn coil.