Faraday's Law
ε = −N·dΦ/dt. Move a magnet near a coil and watch the galvanometer needle.
Key Notes
Faraday's law: the EMF induced in a circuit equals the NEGATIVE rate of change of magnetic flux through it.
For an N-turn coil: ε = −N·dΦ/dt. The minus sign is Lenz's law — encodes opposition.
Any way of changing flux generates EMF: moving the magnet, moving the coil, changing B, deforming the loop, rotating the loop.
Faraday discovered this experimentally (1831) by plunging a magnet through a coil and seeing the galvanometer kick.
EMF is proportional to the RATE of flux change — faster motion ⇒ bigger ε.
Direction of induced current is set by Lenz's law: induced B opposes the change in Φ.
Faraday's law is one of Maxwell's four equations and underlies generators, transformers, induction cooktops, microphones, electric guitars, and metal detectors.
Formulas
Faraday's law (single loop)
Sign follows from choosing a positive sense and applying right-hand rule.
N-turn coil
Multiplies because the same flux change links N turns.
Integral form (Maxwell)
Even where no wire exists, changing B produces a non-conservative E that drives current if a circuit IS there.
Rotating coil (AC generator)
Peak EMF: ε₀ = NBAω.
Important Points
EMF exists even when there is NO current (open circuit) — Faraday's law is about voltage, not current.
Speeding up the motion increases EMF linearly. Doubling the speed ⇒ doubling ε.
A coil rotated in a uniform B at constant ω generates SINUSOIDAL EMF — the underlying principle of every AC power plant.
An induced E is non-conservative: ∮E·dl ≠ 0 in regions of changing B (unlike electrostatic E from charges).
The minus sign in Faraday's law is NOT decorative — it determines the polarity of the induced EMF (Lenz).
Stationary loop in a steady B → no EMF. Even a strong B does nothing unless something changes.
Faraday's Law notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.