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A copper ring is held horizontally and a bar magnet is dropped through the ring with its North pole facing down. The acceleration of the falling magnet is:

Less than g. By Lenz's law, the induced current in the copper ring creates an upward magnetic field opposing the approaching North pole, producing an upward retarding force so a < g.

Physics · Class 12 · JEE / NEET / AP Physics C

Electromagnetic Induction & Lenz's Law

Electromagnetic Induction (EMI)is the production of an electromotive force (EMF) across an electrical conductor in a changing magnetic field.Lenz's Lawdictates that the induced current always opposes the flux change that produced it.

11. Visual Overview & Intuitive Discovery: Electromagnetic Induction & Lenz's Law

In 1831, Michael Faraday demonstrated the first electric generator. A skeptical British politician asked him, "This magnetic coil is an amusing toy, but what practical value will it ever have?" Faraday famously replied: "Sir, I do not know, but one day you will tax it." Today, more than 99% of all electricity consumed on Earth—from nuclear reactors to hydroelectric dams and wind turbines—is generated using Faraday's Law.

Electromagnetic Induction & Motional EMF: Faraday-Lenz Law, Magnetic Flux, Motional EMF, Self-Inductance (L) — Electromagnetic Induction & Motional EMF
Bar magnet entering coil with opposing induced magnetic polarity (Lenz's Law) and conducting rod sliding in magnetic field generating motional EMF ε = Bvl.
1Faraday-Lenz Law — ε = - dΦ_B / dt
2Magnetic Flux — Φ_B = B · A · cos(θ) measured in Webers (Wb = T·m²)
3Motional EMF — ε = B · v · L for a rod of length L moving perpendicular to field B at speed v
4Self-Inductance (L) — Φ = L · I and ε = -L (dI/dt), measured in Henries (H)

Interactive Study Prompts (Click to Explore)

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AI Deep Dive 🪄

22. Physical Mechanism Flowchart: Electromagnetic Induction & Lenz's Law

Electromagnetic Induction & Lenz's Law Step-by-Step Flowchart

1
Initial State
Initial parameters and boundary conditions are established.
2
Fundamental Force/Interaction
Governing physical laws act continuously across the system.
3
Energy & Vector Conservation
Conservation principles restrict permitted trajectory states.
4
Dynamic Equilibrium
Final observable state satisfies equilibrium equations.

Follow the numbered pipeline above. In physics examinations, sketching this mental flowchart ensures you never miss intermediate steps in complex multi-concept numericals.

33. Rigorous Mathematical Proofs & Governing Equations

Derivation — Derivation of Governing Formula for Electromagnetic Induction & Lenz's Law

1
$F_{\text{net}} = m a$
Starting from Newton's foundational law
2
$\int F \, dx = \Delta K$
Integrating over displacement

Energy Stored in an Inductor

U_B = \frac{1}{2} L I^2,\quad u_B = \frac{B^2}{2\mu_0}

$U_B$ = Magnetic potential energy stored in the inductor
$u_B$ = Magnetic energy density per unit volume

Core Physical Variables

Variable	Symbol	SI Unit
Energy	E	Joules (J)
Power	P	Watts (W)

Energy
Symbol
E
SI Unit
Joules (J)
Power
Symbol
P
SI Unit
Watts (W)

44. Transportation: Maglev Trains & Magnetic Eddy Current Braking

Bullet trains in Japan and Germany travel at over 500 km/h with zero physical brake wear. They use Eddy Current Brakes based on Lenz's law. Powerful electromagnets above the rails are switched on. As the conductive copper/aluminum rail rushes through the magnetic field, giant swirling eddy currents are induced in the metal. By Lenz's law, these induced currents create opposing magnetic fields that exert a massive retarding force, slowing the 400-ton train smoothly to a halt without friction pads.

Exam tip: Lenz's Law Nature Analogy: Lenz's law is the universe's way of enforcing Newton's third law in electromagnetism. If the induced current did NOT oppose the original change in magnetic flux, you could nudge a magnet toward a coil, the induced current would attract the magnet faster, generating infinite energy out of nowhere and violating the First Law of Thermodynamics!

55. Solved Standard & Advanced Exam Problems

Exam question · JEE Standard

Sample Question

Exam question · JEE Main & AP Physics

A copper ring is held horizontally and a bar magnet is dropped vertically through the center of the ring. What is the acceleration of the falling magnet while entering the ring?

A.Less than g
B.Equal to g
C.Greater than g
D.Zero

Remember

An induced EMF requires changing magnetic flux, achieved by changing B, area A, or angle θ.
Lenz's law is a direct consequence of the principle of conservation of energy.
Motional EMF ε = BvL arises from the magnetic Lorentz force acting on mobile conduction electrons.
Inductors oppose instantaneous changes in current, acting as electrical inertia.

Check yourself

Question 1
A copper ring is held horizontally and a bar magnet is dropped through the ring with its North pole facing down. The acceleration of the falling magnet is: