Lenz's Law Calculator

Starting from Faraday's law:

$$\varepsilon = -N\frac{\Delta\Phi}{\Delta t}$$

The magnitude of the induced EMF is:

$$|\varepsilon| = N\frac{|\Delta\Phi|}{\Delta t}$$

The induced current in a closed circuit of resistance $$R$$ follows from Ohm's law:

$$I = \frac{|\varepsilon|}{R} = \frac{N|\Delta\Phi|}{R \cdot \Delta t}$$

The power dissipated in the resistance is:

$$P = I^2 R = \frac{\varepsilon^2}{R} = \frac{N^2(\Delta\Phi)^2}{R(\Delta t)^2}$$

Lenz's law determines the current direction: if the external flux through the coil is increasing ($$\Delta\Phi > 0$$), the induced current flows in the direction that creates a magnetic field opposing the increase (counterclockwise when the flux vector points toward you, by the right-hand rule). If the flux is decreasing, the current flows to support the diminishing field (clockwise in the same viewing convention).

This opposition is not merely a convention — it is a direct consequence of energy conservation. Without Lenz's law, the induced current would reinforce the flux change, creating a runaway process that generates energy from nothing. Instead, work must be done against the opposing force to maintain the flux change, and this mechanical work is converted to electrical energy dissipated as heat in the resistance.

Induced EMF is the voltage generated by the changing flux. Induced Current is the EMF divided by the circuit resistance — lower resistance means more current for the same EMF. Power Dissipated is the energy per second converted to heat in the resistance, equaling the mechanical power input needed to sustain the flux change. Current Direction tells you which way the current flows based on whether the flux is increasing or decreasing, following the right-hand rule convention.