# Magnetic damping

Magnetic damping is a form of damping that occurs when a magnetic field moves through a conductor (or vice versa).

## Definition

When a magnetic field (magnet) moves through a conductor an eddy current is induced in the conductor due to the magnetic field's movement. The flow of electrons in the conductor creates an opposing magnetic field to the magnet which results in damping of the magnet and causes heating inside of the conductor similar to heat buildup inside of power cords. The loss of energy used to heat up the conductor is equal to the loss of kinetic energy by the magnet. Eddy currents induced in conductors are much stronger as temperatures approach cryogenic temperatures. This allows for critical damping for cryogenic applications and testing in the aerospace industry.

## Equation

The differential equation of motion of a magnet dropped vertically through or near a conductor, where “M” is the mass of the magnet, “K” is the damping coefficient, “v” is the velocity, “g” is gravity and “a” is the acceleration of the magnet:

${\displaystyle Ma=Mg-Kv}$

As gravitational pull increases, the magnet's acceleration as it falls will tend to increase, except to the extent that the damping coefficient the magnet is experiencing (as a result of the conductor) increases, combined with the extent that the velocity of the magnet also increases— a magnet moving/ falling quickly will have its acceleration (i.e., its increase in speed as it falls) reduced more than one moving/ falling more slowly, and this effect on acceleration will be even more pronounced if the damping coefficient of the conductor is high.

## Uses

• Vehicle braking
• Roller coaster braking
• Elevators
• Near critical damping at cryogenic temperatures