Lenz’s Law of Electromagnetic Induction: Definition & Formula

What is Lenz’s Law?

Lenz’s law of electromagnetic induction states that an induced electromotive force has a direction that opposes the change in magnetic flux that caused it, consistent with Faraday’s law of electromagnetic induction. In a closed circuit, the induced magnetic field produced by the resulting current opposes the change in flux, not necessarily the original field itself. A right-hand grip rule gives loop-current direction after the required induced field is known; Fleming’s right hand rule applies to motional generator cases.

The central question is whether flux through the chosen loop is increasing or decreasing. The examples below apply that test.

If the circuit is closed, the induced electromotive force drives current, and that current produces its own magnetic field.

The induced field acts so that it opposes the change in linked magnetic flux. It can oppose an increasing applied field or reinforce a decreasing applied field.

In case (1), the magnetic field B through a fixed loop is increasing. The induced field therefore points in the opposite direction to reduce that increase.

In case (2), magnetic field B through the loop is decreasing. The induced field points in the same direction as B because it acts to reduce the decrease. In each case, the induced response opposes the change rather than a fixed field direction.

Lenz’s law supplies the direction in Faraday’s induction law. A changing magnetic flux induces an electromotive force in a conductor; current follows only when a closed path exists.

Lenz’s law gives the direction of induced electromotive force and closed-circuit current. The response opposes the change in linked flux. The negative sign in Faraday’s law records this direction relative to chosen positive loop and surface directions.

Flux can change when field magnitude, loop area or loop orientation changes. Relative motion between a magnet and coil is one common way to produce such a change.

The magnitude of induced electromotive force is proportional to the time rate of change of magnetic flux linkage. For N identical turns, the linkage is NΦ when each turn links the same flux Φ.

Lenz’s Law Formula

Lenz’s law states that when changing magnetic flux induces an electromotive force, its polarity would drive a current whose field opposes the flux change. This statement also covers an open circuit, where an electromotive force exists but no sustained current flows.

The negative sign in Faraday’s law indicates opposition under a consistent sign convention: ε = -N dΦ_B/dt. It does not mean that scalar magnitudes are negative. The formula is shown below:

Where:

• ε = Induced emf
• δΦ_B = change in magnetic flux through one turn
• N = number of turns in the coil

Lenz’s Law and Conservation of Energy

Lenz’s law is consistent with conservation of energy. When a closed circuit carries induced current, its magnetic effect resists the change in flux, so an external agent must supply work to sustain that change.

Consider pushing a magnet towards a conducting coil connected to a load.

The increasing flux induces current whose field repels the approaching pole. The person or mechanism moving the magnet must work against this electromagnetic force.

That mechanical work becomes electrical energy in the circuit and, depending on the load, stored field energy or heat. The induced electromotive force and total circuit impedance determine current magnitude, so the original claim of automatic doubling has no basis.

If the induced force instead assisted the approach, the system could increase electrical output while requiring less mechanical input.

Such self-assistance would create energy without a matching input. Lenz’s law prevents that result because the induced response opposes the change that transfers energy into the electromagnetic system.

Mechanical induction examples can also exhibit an action-reaction force pair between the magnet and coil, but Newton’s third law is not the definition or general derivation of Lenz’s law.

The induced field need not be equal and opposite to the applied field. Its magnitude depends on flux-change rate and circuit impedance, and its direction is the one that opposes the change in flux.

Lenz’s Law Explained

Consider a closed coil viewed from the side facing the magnet in these two cases:

Case 1: When a magnet is moving towards the coil.

When the magnet’s north pole approaches the closed coil, magnetic flux through the coil increases. Faraday’s law gives an induced electromotive force, which drives current through the closed circuit and creates a magnetic field.

Under Lenz’s law, the induced field opposes the increase in flux. The coil face nearest the approaching north pole therefore behaves as a north pole, producing a repulsive force.

Use the right-hand grip rule with the thumb pointing out of the coil’s north face. Viewed from the approaching magnet, the induced conventional current is anticlockwise.

Case 2: When a magnet is moving away from the coil

When the magnet’s north pole moves away from the closed coil, the magnetic flux through the coil decreases. Faraday’s law again gives an induced electromotive force, which drives current and creates a magnetic field.

Under Lenz’s law, the induced field opposes the decrease in flux. The coil face nearest the receding north pole therefore behaves as a south pole, producing an attractive force.

Use the right-hand grip rule with the thumb pointing into the coil’s south face. Viewed from the magnet, the induced conventional current is clockwise.

To relate coil current and magnetic field, use the right-hand grip rule. Curl the right-hand fingers in the conventional-current direction around the coil; the thumb points towards the coil’s north face and along its internal magnetic field.

The two cases can be summarised as follows:

• If magnetic flux Ф through a closed coil increases in one direction, induced current produces flux in the opposite direction, as shown below. Use the right-hand grip rule to convert the required field direction into current direction.

• If magnetic flux Ф through a closed coil decreases, induced current produces flux in the same direction as the original flux to oppose that decrease, as shown below.

Lenz’s Law Applications

Lenz’s law explains the direction of induced voltage, current and force in these applications:

• In an inductor, self-induced electromotive force has a polarity that opposes a change in current. Work supplied while current rises is stored in the magnetic field, with ideal stored energy W = ½LI². When current falls, the field can return that energy to the circuit.
• The law provides the physical direction represented by the negative sign in Faraday’s induction law, provided flux and loop directions use one consistent sign convention.
• In a loaded generator, induced current produces reaction torque that opposes the driving rotation, so the prime mover must supply mechanical input. Rotating electric motors also generate back electromotive force that opposes the applied voltage.
• Electromagnetic brakes use induced eddy currents to create drag against motion. Induction cooktops use changing flux to induce cookware currents whose resistive losses produce heat.

State Lenz’s Law

Lenz’s law states that induced electromotive force has the direction that would drive current whose magnetic effect opposes the change in magnetic flux that caused it.

Physicist Heinrich Friedrich Emil Lenz stated the direction principle in 1834, and the law bears his name. Energy conservation provides its general basis. Induction systems may exert equal and opposite mechanical forces on interacting bodies, while Newton’s third law describes those forces rather than the complete induction principle.