Lenz's Law
Induced current opposes the change in flux — repels approaching magnet, attracts retreating.
Key Notes
Lenz's law: the direction of induced current is such that it OPPOSES the change producing it.
If flux INTO the loop is increasing, induced current circulates so that its field points OUT of the loop (to oppose the increase).
If flux is decreasing, induced current creates a field in the SAME direction as the (decreasing) original field — trying to maintain it.
This is a direct consequence of CONSERVATION OF ENERGY — if induced current AIDED the change, energy would appear from nothing.
When you push a magnet toward a coil, the induced current makes the coil-face FACING the magnet a repelling pole (same pole). You feel resistance — that mechanical work becomes electrical energy.
Pulling the magnet away makes the facing coil-face attracting (opposite pole) — again the force opposes your motion.
Lenz's law sets the SIGN of the EMF in Faraday's law: ε = −N·dΦ/dt.
Formulas
Lenz / Faraday combined
The negative sign IS Lenz's law mathematically encoded.
Energy interpretation
Mechanical work done against opposing force = electrical energy dissipated.
Force on a sliding rod (motional)
Magnetic braking force always opposes velocity.
Important Points
Lenz's law is NOT independent — it follows from energy conservation. If induced current aided the change, energy would be generated from nothing.
Eddy-current brakes, induction cooktops, transformer iron losses, and metal detectors all rely on Lenz-law forces.
A magnet falling through a copper pipe takes much longer than free-fall — the induced eddies brake it. Same magnet through a slotted pipe → free-fall, because eddy paths are broken.
The induced current is a RESPONSE — it doesn't START until the flux is already changing.
Rule of thumb: 'Nature is lazy' — it always opposes any change in flux through any closed loop.
Lenz's law DOES NOT say the current cancels the original flux entirely — only the CHANGE in flux.
Lenz'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.