Magnetic dipole

Magnetic field lines of different magnetic dipoles: point dipole, magnetic poles , circular conductor loop and solenoid .

A magnetic dipole is the simplest observed form in which magnetism occurs. All more complicated magnetic structures can be composed of dipoles .

Absence of magnetic charges

Magnetic field lines have no ends. The magnetic field is always source-free, i. H. divergence-free .

There is speculation about magnetic monopoles (analogous to individual positive or negative electrical charges), but none have yet been discovered. In the case of commercially available bar or horseshoe magnets, as well as long magnet coils, the two ends can be addressed approximately individually as the magnetic north or south pole . When trying to separate the poles of a magnet by breaking it apart in the middle, a new north and south pole emerges at the intersection, so that each fragment forms a dipole again.

Occurrence and meaning of magnetic dipoles

According to classical electrodynamics , a magnetic dipole field can be generated by a circular current that flows around an area . Its magnetic dipole moment (alternatively also ) is: ${\ displaystyle I}$ ${\ displaystyle {\ vec {\ Omega}}}$ ${\ displaystyle {\ vec {m}}}$ ${\ displaystyle {\ vec {\ mu}}}$

{\ displaystyle {\ vec {m}} = I {\ vec {\ Omega}}}

In addition, all previously known elementary particles , provided they are electrically charged and have an intrinsic angular momentum ( spin ) other than zero , are also magnetic dipoles with a different dipole moment depending on the type of particle. This includes quarks and electrons and thus most of the atomic nuclei and atoms built from them . These dipoles are important in atomic , nuclear and elementary particle physics .

The observation of directional quantization , according to which an elementary dipole moment can only assume certain angles to an external magnetic field, has contributed significantly to the elucidation of the structure of particles and atoms. See also: magnetic moment of particles and nuclei , Stern-Gerlach experiment , normal and anomalous Zeeman effect , nuclear and electron spin resonance .

Field of the dipole

A magnetic dipole creates a magnetic field, given by the magnetic flux density at a location further away ${\ displaystyle {\ vec {r}}}$

{\ displaystyle {\ vec {B}} ({\ vec {r}}) \, = \, {\ frac {\ mu _ {0}} {4 \ pi r ^ {2}}} \, {\ frac {3 {\ vec {r}} ({\ vec {m}} \ cdot {\ vec {r}}) - {\ vec {m}} r ^ {2}} {r ^ {3}}} \.}

${\ displaystyle r}$ is the amount of , is the magnetic field constant and is the distance between the spherical surface . ${\ displaystyle | {\ vec {r}} |}$ ${\ displaystyle {\ vec {r}}}$ ${\ displaystyle \ mu _ {0}}$ ${\ displaystyle 4 \ pi r ^ {2}}$ ${\ displaystyle r}$

This formula applies regardless of the shape and size of the current loop, the magnetic coil, the bar magnet or the atom, if it is large compared to their spatial expansion. ${\ displaystyle r}$

In an external magnetic field, the torque acts on a magnetic dipole ${\ displaystyle {\ vec {B}}}$

{\ displaystyle {\ vec {M}} = {\ vec {m}} \ times {\ vec {B}},}

and it has a potential energy that depends on the angle to the field direction

{\ displaystyle E _ {\ mathrm {pot}} = - {\ vec {m}} \ cdot {\ vec {B}}.}

If the field is inhomogeneous , the force acts primarily

{\ displaystyle {\ vec {F}} = \ left ({\ vec {\ nabla}} \ otimes {\ vec {B}} \ right) {\ vec {m}}}

with the Nabla operator . ${\ displaystyle \ nabla}$

The magnetic properties of a piece of matter are determined by the magnetic dipoles that are already present in it with a constant size (as in ferro- , antiferro- and paramagnetism ) or are only generated when the field is switched on ( diamagnetism ).

annotation

↑ Magnetic monopoles as elementary particles are not fundamentally excluded, they are predicted by some great unified theories . Apparent "magnetic monopoles" have been detected as quasiparticles in certain solids (see web links); however, there are always the same number of equally strong north and south poles.

Individual evidence

↑ Wolfgang Nolting: Basic Course Theoretical Physics 3. Chapter 3.3.2. 8th edition, Springer-Verlag Berlin Heidelberg New York, ISBN 978-3-540-71251-0 .

literature

Horst Stöcker: Pocket book of physics. 4th edition, Verlag Harry Deutsch, Frankfurt am Main, 2000, ISBN 3-8171-1628-4 .

[1] Magnetic monopoles as elementary particles are not fundamentally excluded, they are predicted by some great unified theories . Apparent "magnetic monopoles" have been detected as quasiparticles in certain solids (see web links); however, there are always the same number of equally strong north and south poles.

[2] Wolfgang Nolting: Basic Course Theoretical Physics 3. Chapter 3.3.2. 8th edition, Springer-Verlag Berlin Heidelberg New York, ISBN 978-3-540-71251-0 .