Lenz's Law

Interprets induced polarity as opposition to magnetic flux change. Theory, formulas, worked examples and interactive graphs.

Conceptual context

Lenz's law gives the physical direction of electromagnetic induction. Faraday tells how large the induced emf is; Lenz tells with what polarity it appears in order to oppose the flux change that produces it.

This leaf explains why induction does not oppose magnetic field merely by existing, but opposes linked flux change. The central quantity is $\varepsilon_{ind}$, but its reading depends on $\Delta \Phi_B$, $r_\Phi$, and the chosen sign convention.

[!NOTE] Lenz is not a new force. It is the sign reading that prevents induction from spontaneously reinforcing the change that creates it.

🟢 Essential level

When magnetic flux linked with a circuit changes, induced emf appears. Lenz's law states that this emf has a direction tending to oppose the flux change. If flux increases, the induced response tends to slow that increase; if flux decreases, it tends to sustain it.

The key idea is opposition to change, not opposition to field. A loop near a stationary magnet may have flux, but it does not need to generate sustained emf. When the magnet moves closer or farther away, the circuit responds to flux change.

This rule also protects energy conservation. If induced current reinforced the change producing it, the system could amplify itself without external work. Lenz indicates that maintaining the change requires energy supplied from outside. This is why dropping a magnet down a copper tube falls noticeably slower than dropping a non-magnetic object of the same weight: induced currents in the tube oppose the magnet's motion.

[!WARNING] Do not first ask where the field points. Ask whether linked flux increases or decreases relative to a chosen normal.

🔵 Formal level

Basic formulas

Lenz's law appears in the average Faraday form through the negative sign:

Lenz law in Faraday form

That negative sign is not an algebraic detail: it shows that induced emf opposes the flux change producing it rather than reinforcing it, which is exactly what keeps the process consistent with energy conservation.

Real student questions

Does Lenz always oppose the magnetic field? No. It opposes linked flux change. If field is present but not changing, there is no average induced emf.

Why does the negative sign matter? It fixes physical polarity of $\varepsilon_{ind}$. Without the sign, only a voltage without induced direction remains.

Does induced current always cancel the change? No. It tends to oppose it, but intensity depends on resistance, coupling, and available energy.

What if I do not know the normal direction? Choose one normal and keep it. Changing the normal changes signs, but not physics if you stay coherent.

Final synthesis

Lenz's law states that induction is oriented against the flux change causing it. $\varepsilon_{ind}$ has physical meaning only if the sign of $\Delta \Phi_B$ or $r_\Phi$ is preserved and induced polarity is interpreted.