Magnet

Linear magnet

A linear magnet whose magnetization is proportional to the magnetic field¹, or equivalently

⃗𝐌=𝜒𝑚⃗𝐇

where ⃗𝐇 is the H-field and 𝜒𝑚 is the empirically determined magnetic susceptibility, and

• 𝜒𝑚 >0 for Paramagnetism
• 𝜒𝑚 <0 for Diamagnetism

The permeäbility of a linear magnet is then

𝜇=𝜇0(1+𝜒𝑚)>0

and the magnetic field is related to ⃗𝐇 by

⃗𝐇=𝜇⃗𝐁

Homogenous linear magnet

In case a volume Ω is occupied by a homogenous linear magnet, i.e. one with constant 𝜒𝑚 we have

⃗𝐉𝑏=𝜒𝑚⃗𝐉𝑓

and so if there is no free current there is also no bound current, meaning all bound current must be found on the surface 𝜕Ω.

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tidy | en | SemBr

Footnotes

1. Note that the electric field includes that caused by the magnet itself. ↩