Statement of Lenz's Law
In 1834, the German physicist Heinrich Friedrich Lenz deduced a rule that fixes the polarity of the induced emf in a clear and concise fashion. The statement, as given in NCERT §6.5, is precise and worth memorising verbatim:
The polarity of induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produced it.
The NIOS module phrases the same idea operationally: when a current is induced in a conductor, the direction of the current will be such that its magnetic effect opposes the change that induced it. The single load-bearing word is oppose. Whatever the cause of the flux change — a magnet pushed in, a magnet pulled out, a current switched on in a neighbouring coil — the induced current arranges itself to fight that change.
| Cause of flux change | Flux behaviour | Induced current opposes by… |
|---|---|---|
| North pole approaching coil | Flux through coil increasing | Presenting a north pole to repel the magnet |
| North pole receding from coil | Flux through coil decreasing | Presenting a south pole to attract (retard) the magnet |
| Neighbouring current switched on | Flux rising from zero | Driving current that opposes the rise |
| Neighbouring current switched off | Flux falling to zero | Driving current that opposes the fall |
The Minus Sign in Faraday's Law
Faraday's law gives the induced emf as the time rate of change of magnetic flux. The complete statement, combining magnitude and direction, carries a negative sign:
$$ \varepsilon = -\frac{d\Phi_B}{dt} $$
For a closely wound coil of $N$ turns, where the same flux threads every turn, this becomes:
$$ \varepsilon = -N\frac{d\Phi_B}{dt} $$
NCERT is explicit that the negative sign shown here is Lenz's law: it represents the effect by which the induced emf opposes the change in flux. The magnitude of the emf comes entirely from $|d\Phi_B/dt|$; the minus sign is a bookkeeping device that encodes the direction. NIOS states the same: the negative sign signifies opposition to the cause.
As the north pole approaches, flux increases; the induced current is counter-clockwise (seen from the magnet), so the coil face nearest the magnet becomes a north pole and repels the magnet, opposing its motion. (After NCERT Fig. 6.6.)
Magnet Approaching and Receding
NCERT works through the canonical case of Experiment 6.1. When the north pole of a bar magnet is pushed towards a closed coil, the magnetic flux through the coil increases. The induced current must oppose this increase, which is possible only if it flows counter-clockwise with respect to an observer on the magnet's side. The magnetic moment of that current then presents a north polarity towards the approaching north pole — like poles repel, so the coil pushes back on the magnet.
The receding case is the mirror image and is a favourite NEET trap. When the north pole is withdrawn, the flux through the coil decreases. To counter that decrease, the induced current reverses to flow clockwise, so the coil now presents a south pole to the retreating north pole. The resulting attractive force pulls back on the magnet, again opposing its motion. The induced current opposes the change, not the field itself; that is why it flips sign between approach and withdrawal.
As the north pole recedes, flux decreases; the induced current reverses (clockwise from the magnet side), so the coil face becomes a south pole and attracts the receding magnet, again opposing its motion.
Lenz's law is energy conservation, not a separate axiom
A common error is to treat Lenz's law as an independent postulate sitting alongside Faraday's law. It is not. NCERT derives it from the impossibility of perpetual motion: the opposition the induced current offers is precisely what conservation of energy demands. The minus sign in $\varepsilon = -d\Phi_B/dt$ is not arbitrary — it is the only sign consistent with energy bookkeeping.
Sign check: when a magnet's pole recedes, flux decreases, and the induced current flips to attract the magnet. Do not assume the induced pole stays fixed — it depends on whether flux is rising or falling.
Why Lenz's Law Is Energy Conservation
NCERT offers a clean reductio argument. Suppose the induced current ran the opposite way to what Lenz's law predicts — so that the coil presented a south pole to an approaching north pole. The magnet would then be attracted towards the coil, accelerating ever faster. A gentle initial push would set it moving, and its velocity and kinetic energy would grow without limit, with no external energy supplied. One could then build a perpetual-motion machine. Since this violates the law of conservation of energy, it cannot happen; the induced current must therefore oppose the motion, exactly as Lenz's law states.
NIOS makes the same point with its memorable phrasing: "we are not going to get something for nothing." The opposition is nature's way of refusing a free lunch. This is why the Points to Ponder note in NCERT records that in a closed circuit, currents are induced so as to oppose the changing flux precisely as per the law of conservation of energy.
Lenz's law only fixes the sign of the emf that Faraday's law already gives in magnitude. Revise the rate-of-change rule before relying on the minus sign.
Energy Bookkeeping and Joule Heating
Once we accept that the induced current opposes the magnet's motion, a natural question follows: where does the energy go? In the correct configuration, the bar magnet experiences a repulsive force from the induced current as it approaches. To keep moving the magnet, a person must do mechanical work against this force.
That work does not vanish. As NCERT states, the energy spent by the person is dissipated as Joule heating produced by the induced current in the resistance of the loop. The mechanical energy input is converted, via the induced emf and current, into electrical energy and finally into heat. NIOS states this directly: the work done in pushing the magnet "shows up as electrical energy in the ring." This is the complete energy ledger of electromagnetic induction.
Trace the energy when a magnet is pushed steadily into a closed coil.
Mechanical work by the agent $\rightarrow$ overcomes the repulsive force from the induced current $\rightarrow$ stored momentarily as electrical energy in the induced emf $\rightarrow$ dissipated as Joule heat $I^2 R t$ in the coil's resistance. No energy is created or destroyed; Lenz's law guarantees the books balance.
Eddy Currents
Induced currents are not confined to thin wire loops. When a solid conductor — a sheet or plate — sits in a changing magnetic field, closed loops of induced current are set up within the body of the conductor itself. NIOS §19.1.3 calls these eddy currents (also Foucault currents, after their discoverer), because they swirl like eddies or whirlpools. They flow in closed paths in a plane perpendicular to the changing flux.
Their direction is fixed by Lenz's law: they oppose the flux change that produces them. Because metallic bodies offer little resistance, eddy currents can be large and dissipate substantial energy as heat. In transformers and motor cores this is wasteful, so the cores are laminated — built from thin insulated strips rather than one solid block — to break up the current paths and reduce the loss.
With $B$ into the page and increasing, eddy currents circulate anticlockwise to oppose the rising flux, exactly as Lenz's law requires. (After NIOS Fig. 19.1.3.)
Eddy currents are not purely a nuisance. NIOS lists useful applications: induction furnaces use them to melt and alloy metals in vacuum, and electric brakes use them to stop electric trains smoothly, the opposing force doing the braking work.
Applying Lenz's Law to Loops
For loops entering or leaving a field region, NCERT Example 6.4 gives the working method: identify whether flux is increasing or decreasing, then choose the current sense that opposes that change. A rectangular loop moving into a field (flux increasing) carries current in the sense that opposes the increase; a loop moving out (flux decreasing) reverses. Crucially, when a loop is wholly inside or wholly outside the field region, the flux is not changing, so no current is induced.
| Situation (field into page) | Flux | Induced current |
|---|---|---|
| Loop entering the field region | Increasing | Anticlockwise (opposes increase) |
| Loop leaving the field region | Decreasing | Clockwise (opposes decrease) |
| Loop fully inside the field | Constant | Zero — no flux change |
| Loop fully outside the field | Zero | Zero — no flux change |
For the rectangular-versus-circular comparison in NCERT Example 6.5(c), the induced emf is constant only for the rectangular loop leaving the field, because its rate of change of overlapping area is uniform; for a circular loop the overlapping area changes non-uniformly, so the emf varies. Lenz's law fixes the direction; the geometry fixes whether the magnitude is steady.
Lenz's Law in One Glance
- Lenz's law: induced emf is such that the induced current opposes the flux change that produced it.
- The negative sign in $\varepsilon = -d\Phi_B/dt$ is Lenz's law — it encodes direction, not magnitude.
- Approaching magnet $\rightarrow$ flux increases $\rightarrow$ coil repels it; receding magnet $\rightarrow$ flux decreases $\rightarrow$ coil attracts it.
- Lenz's law is a consequence of conservation of energy, not a separate axiom; the opposite sign would allow perpetual motion.
- Work done against the opposing force is dissipated as Joule heating in the loop.
- Eddy currents obey Lenz's law; laminating cores reduces them, and they are exploited in induction furnaces and electric brakes.