In 1834, Heinrich Lenz published his law specifying the physical direction of induced electric currents in electromagnetic induction.

Statement & Vector Formula of Lenz’s Law¶

“An induced electric current flows in a direction such that its magnetic field opposes the change in magnetic flux that produced it.”

In Faraday’s Law, Lenz’s Law is represented by the minus sign ($-$):

$$\mathcal{E} = -\frac{d\Phi_B}{dt}$$

Direct Consequence of Energy Conservation¶

If the sign were positive ($+$), an induced current would create magnetic flux in the same direction as the change, creating a runaway feedback loop generating infinite free energy!

Thus, Lenz’s Law is a direct expression of the Conservation of Energy in electrodynamics.