Lenz's law

Direction of induced effects

Faraday's law tells the magnitude of induced emf, but its negative sign encodes direction:

mathcal{E}=-rac{dPhi_B}{dt}

Lenz's law states that the induced current or induced emf acts in a direction that opposes the change in magnetic flux that produced it.

It does not necessarily oppose the magnetic field itself. It opposes the change in flux.

Opposing an increase or decrease

If magnetic flux through a loop is increasing into the page, the induced current creates a magnetic field out of the page to oppose the increase. If flux into the page is decreasing, the induced current creates a magnetic field into the page to oppose the decrease.

This distinction is essential. The induced field may point with or against the original field depending on whether flux is decreasing or increasing.

Using the right-hand rule

To find induced current direction, first determine the direction of the induced magnetic field needed to oppose the flux change. Then use the right-hand rule for a current loop: curl your fingers in the current direction, and your thumb points in the loop's magnetic field direction.

If the induced field must point out of the page, current is counterclockwise. If it must point into the page, current is clockwise.

Energy conservation

Lenz's law is a consequence of energy conservation. If induced currents aided the flux change instead of opposing it, a small change would reinforce itself, creating energy from nothing. Opposition ensures that external work is required to maintain the change.

For example, pushing a conducting loop into a magnetic field induces a current whose magnetic force resists the motion. You must do work, and that work becomes electrical energy and heat.

Moving magnet and coil

When a north pole of a magnet approaches a conducting loop, the magnetic flux through the loop increases. The loop induces a current that makes the near face act like a north pole, repelling the approaching magnet. When the magnet moves away, the loop reverses current, attracting the magnet and opposing the separation.

In both cases, the induced effect resists the relative motion that changes flux.

Eddy currents

Changing magnetic flux in a bulk conductor can induce circulating currents called eddy currents. These currents produce magnetic fields and dissipate energy as heat.

Eddy currents are useful in induction cooktops, metal detectors, and magnetic braking. They can be undesirable in transformer cores and motors, where they waste energy. Laminated cores reduce eddy currents by interrupting large current loops.

Magnetic braking

In magnetic braking, a conductor moves through a magnetic field, inducing eddy currents. The magnetic forces on these currents oppose motion, slowing the conductor without contact. The kinetic energy becomes thermal energy in the conductor.

This technique is used in some trains, amusement rides, and laboratory demonstrations.

Back emf

Motors also show Lenz's law. As a motor spins, it acts partly like a generator and produces a back emf opposing the applied voltage. The back emf grows with speed, reducing current. When a motor is first started, back emf is small, so current can be large.

The big idea

Lenz's law gives the direction of induction: induced currents oppose the change in magnetic flux that causes them. This opposition is a direct expression of energy conservation. It explains magnetic braking, eddy currents, transformer losses, motor back emf, and the effort required to move conductors through magnetic fields.