# 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.

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## 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:

$Ma = Mg - KV\,$
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## Uses

• Vehicle braking
• Roller coaster braking
• Elevators
• Near critical damping at cryogenic temperatures
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## Observing Magnetic Dampening

Magnetic damping can be observed easily due to the development of strong magnets made of neodymium and other rare earth metals. To observe magnetic damping with a minimum of materials and effort, use any length of copper tubing and a neodymium magnet with a smaller diameter than the tube. Ideally the neodymium magnet will have a diameter only slightly smaller than the tube to maximize the magnetic field. Hold the tube vertically and drop the magnet through it to see magnetic damping at work.

Dropping a chained line of these magnets through the copper tube shows magnetic damping, however connecting the magnets in a ring before dropping them shows minimal magnetic damping. This is due to the collapse of the magnetic field as the north and south poles of the chained magnet are connected.

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## Dangers

Neodymium magnets larger than 1.5 cm are very strong and should be handled with extreme care since they can shatter at high velocities, neodymium magnets of this size can also pinch and even break bones as they are attracted to other magnets or metals.

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## Availability

Radially magnetized neodymium cylinders ranging from 0.1 to 2 cm diameter are readily available for purchase online.

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