Lenz's law

The Induced current is the current generated in a wire due to change in magnetic flux. An example of the induced current is the current produced in the generator which involves rapidly rotating a coil of wire in a magnetic field.

It is a qualitative law that specifies the direction of induced current, but states nothing about its magnitude. Lenz's law predicts the direction of many effects in electromagnetism, such as the direction of voltage induced in an inductor or wire loop by a changing current, or the drag force of eddy currents exerted on moving objects in the magnetic field.

Lenz's law may be seen as analogous to Newton's third law in classical mechanics and Le Chatelier's principle in chemistry.

Definition

Lenz's law states that:

The current induced in a circuit due to a change in a magnetic field is directed to oppose the change in flux and to exert a mechanical force which opposes the motion.

Lenz's law is contained in the rigorous treatment of Faraday's law of induction (the magnitude of EMF induced in a coil is proportional to the rate of change of the magnetic flux), where it finds expression by the negative sign:

$${\displaystyle \mathcal{E}=-\frac{\mathrm{d}{\mathrm{\Phi }}_{\mathbf{B}}}{\mathrm{d}t},}$$

which indicates that the induced electromotive force ${\displaystyle \mathcal{E}}$ and the rate of change in magnetic flux ${\displaystyle {\mathrm{\Phi }}_{\mathbf{B}}}$ have opposite signs.

This means that the direction of the back EMF of an induced field opposes the changing current that is its cause. D.J. Griffiths summarized it as follows: Nature abhors a change in flux.

If a change in the magnetic field of current i₁ induces another electric current, i₂, the direction of i₂ is opposite that of the change in i₁. If these currents are in two coaxial circular conductors ℓ₁ and ℓ₂ respectively, and both are initially 0, then the currents i₁ and i₂ must counter-rotate. The opposing currents will repel each other as a result.

Example

Magnetic fields from strong magnets can create counter-rotating currents in a copper or aluminium pipe. This is shown by dropping the magnet through the pipe. The descent of the magnet inside the pipe is observably slower than when dropped outside the pipe.

When a voltage is generated by a change in magnetic flux according to Faraday's law, the polarity of the induced voltage is such that it produces a current whose magnetic field opposes the change which produces it. The induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant. The direction of an induced current can be determined using the right-hand rule to show which direction of current flow would create a magnetic field that would oppose the direction of changing flux through the loop. In the examples above, if the flux is increasing, the induced field acts in opposition to it. If it is decreasing, the induced field acts in the direction of the applied field to oppose the change.