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A useful tool for dealing with high frequency magnetic effects is the complex permeability. While at low frequencies in a linear material the magnetic field and the auxiliary magnetic field are simply proportional to each other through some scalar permeability, at high frequencies these quantities will react to each other with some lag time. [36]
Assuming the external magnetic field is uniform and shares a common axis with the paramagnet, the extensive parameter characterizing the magnetic state is , the magnetic dipole moment of the system. The fundamental thermodynamic relation describing the system will then be of the form U = U ( S , V , I , N ) {\displaystyle U=U(S,V,I,N)} .
Strip of permalloy. Permalloy is a nickel–iron magnetic alloy, with about 80% nickel and 20% iron content.Invented in 1914 by physicist Gustav Elmen at Bell Telephone Laboratories, [1] it is notable for its very high magnetic permeability, which makes it useful as a magnetic core material in electrical and electronic equipment, and also in magnetic shielding to block magnetic fields.
The magnetic potential energy per unit volume (i.e. magnetic energy density) of the paramagnet (or diamagnet) in the magnetic field is: = = +, the negative gradient of which is the magnetic force on the paramagnet (or diamagnet) per unit volume (i.e. force density).
In other words, the easy axis is an energetically favorable direction of spontaneous magnetization. Because the two opposite directions along an easy axis are usually equivalently easy to magnetize along, the actual direction of magnetization can just as easily settle into either direction, which is an example of spontaneous symmetry breaking.
The high permeability of mu-metal provides a low reluctance path for magnetic flux, leading to its use in magnetic shields against static or slowly varying magnetic fields. Magnetic shielding made with high-permeability alloys like mu-metal works not by blocking magnetic fields but by providing a path for the magnetic field lines around the ...
Magnetic field (green) created by a current-carrying winding (red) in a typical magnetic core transformer or inductor, with the iron core C forming a closed loop, possibly with air gaps G in it. The drawing shows a section through the core. The purpose of the core is to provide a closed high permeability path for the magnetic field lines.
They also have high magnetic permeability. These so-called ceramic magnets are cheap, and are widely used in household products such as refrigerator magnets . The maximum magnetic field B is about 0.35 tesla and the magnetic field strength H is about 30–160 kiloampere turns per meter (400–2000 oersteds ). [ 33 ]