Physics & Mechanics

Lenz's Law Calculator

Calculate induced EMF and determine the polarity and direction of induced current opposing the change in magnetic flux.

Wb/s
Induced EMF (ε)
-50
DirectionOpposes increase (Counter-clockwise)

Calculated locally in your browser. Fast, secure, and private.

The Law of Conservation in Magnetism

Lenz's Law, named after Russian physicist Heinrich Lenz, is the companion to Faraday's Law. While Faraday tells us how much voltage is induced, Lenz tells us the direction of the induced current.

It states that the direction of an induced current is always such that it creates a magnetic field that opposes the change that produced it. This is essentially the electrical version of Newton's Third Law (Action and Reaction).

Understanding the Opposition

  • If you move a North pole toward a coil: The coil will induce a current that creates its own North pole to push back against the magnet.
  • If you pull the North pole away: The coil will induce a current that creates a South pole to pull it back.

In both cases, the coil fights against whatever you are trying to do. This ensures that energy is conserved; you must perform mechanical work to generate electrical energy.

The Formula (Conceptual)

E=NdΦdt\begin{aligned} \mathcal{E} = -N \cdot \frac{d\Phi}{dt} \end{aligned}

Where:
E\mathcal{E}=
Induced EMF
N=
Number of turns
dΦ/dtd\Phi/dt=
Rate of change of magnetic flux
-=
The negative sign represents Lenz's Law (opposition)

Example Application

Imagine a metal ring falling through a magnetic field.

  1. As it enters the field, flux increases.
  2. Lenz's law says the ring will induce a current to push back.
  3. This magnetic "push back" creates a braking force that slows the ring down. This is the principle behind Eddy Current Braking used in roller coasters and high-speed trains.

Frequently Asked Questions

Without that negative sign, induced currents would aid the change in flux. This would create a runaway feedback loop where a small movement creates infinite energy, violating the First Law of Thermodynamics.

When a solid piece of metal (like a plate) moves through a magnetic field, Lenz's law causes swirls of current to form inside the metal itself. these are called 'eddy currents' and they create strong magnetic drag.

Yes, indirectly. The induced currents (eddy currents) encounter resistance in the metal, which converts some of the mechanical energy into heat via Joule heating.