## Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

## diamagnetic levit

A substance that is diamagnetic repels a magnetic field. All materials have diamagnetic properties, but the effect is very weak, and is usually overcome by the object's paramagnetic or ferromagnetic properties, which act in the opposite manner. Any material in which the diamagnetic component is strongest will be repelled by a magnet.

Earnshaw's theorem does not apply to diamagnets. These behave in the opposite manner to normal magnets owing to their relative permeability of μr < 1 (i.e. negative magnetic susceptibility).

Diamagnetic levitation can be used to levitate very light pieces of pyrolytic graphite or bismuth above a moderately strong permanent magnet. As water is predominantly diamagnetic, this technique has been used to levitate water droplets and even live animals, such as a grasshopper, frog and a mouse.[3] However, the magnetic fields required for this are very high, typically in the range of 16 teslas, and therefore create significant problems if ferromagnetic materials are nearby.

The minimum criterion for diamagnetic levitation is $B frac{dB}{dz} = mu_0 , ho , frac{g}{chi}$, where:

• $chi$ is the magnetic susceptibility
• $ho$ is the density of the material
• $g$ is the local gravitational acceleration (−9.8 m/s2 on Earth)
• $mu_0$ is the permeability of free space
• $B$ is the magnetic field
• $frac{dB}{dz}$ is the rate of change of the magnetic field along the vertical axis.

Assuming ideal conditions along the z-direction of solenoid magnet:

• Water levitates at $B frac{dB}{dz} approx 1400 mathrm{T^2/m}$
• Graphite levitates at $B frac{dB}{dz} approx 375 mathrm{T^2/m}.$

#### Diamagnetically-stabilized levitation

A permanent magnet can be stably suspended by various configurations of strong permanent magnets and strong diamagnets. When using superconducting magnets, the levitation of a permanent magnet can even be stabilized by the small diamagnetism of water in human fingers.

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