Lenz’s Law Calculator

Calculate the Induced Electromotive Force ($\mathcal{E}$)

Inputs & Calculation

Number of Turns ($N$)

Change in Magnetic Flux ($\Delta \Phi$) (Wb)

Change in Time ($\Delta t$) (s)

Calculation Output

The formula for Lenz’s Law is:

\mathcal{E} = -N \frac{\Delta \Phi}{\Delta t}

Step 1: Substitution

\text{Enter values and click ‘Calculate’}

Induced EMF ($\mathcal{E}$)

— V

Description: Lenz’s Law

Lenz’s Law, formulated by Heinrich Lenz, is an essential principle in electromagnetic induction that determines the direction of the induced current (and thus the induced electromotive force, $\mathcal{E}$).

It states that the direction of the induced current is always such that it opposes the change in magnetic flux ($\Delta \Phi$) that produced it. This principle is mathematically represented by the negative sign in Faraday’s Law of Induction:

\mathcal{E} = -N \frac{\Delta \Phi}{\Delta t}

Conservation of Energy:

Lenz’s Law is a manifestation of the law of conservation of energy. If the induced current aided the change in flux, the induced emf would continuously increase the magnetic field, leading to an infinite increase in energy without external work, which is impossible. By opposing the change, work must be done (e.g., moving a magnet) to maintain the current, thus ensuring energy conservation.

Real-World Applications:

Electric Generators: The induced current opposes the rotation, requiring a continuous mechanical energy input.
Eddy Current Brakes: Used in high-speed trains, the induced currents create a magnetic field that opposes the motion, providing a smooth, non-contact braking force.
Induction Cooking: Oscillating magnetic fields induce currents in metal pots, heating the cookware itself.

How to Use the Calculator

Number of Turns ($N$): Enter the number of wire loops in the coil. This must be a positive integer.
Change in Magnetic Flux ($\Delta \Phi$): Enter the total change in magnetic flux passing through the coil in Webers (Wb). This can be positive or negative.
Change in Time ($\Delta t$): Enter the time interval over which the flux change occurred in seconds (s). This must be a positive value greater than zero.
Click the “Calculate Induced EMF” button to view the result.
Interpreting the Result ($\mathcal{E}$): The output, $\mathcal{E}$ (induced EMF in Volts, V), will have a sign:
- A positive $\mathcal{E}$ means the induced current flows in the direction of the established coil winding reference (often arbitrary, but consistently used).
- A negative $\mathcal{E}$ simply confirms Lenz’s Law—the induced EMF and its resulting current oppose the original flux change.