# Aharonov–Casher effect

The Aharonov–Casher effect is a quantum mechanical phenomenon in which a traveling magnetic dipole is affected by an electric field. It is dual to the Aharonov–Bohm effect, in which the quantum phase of a charged particle depends upon which side of a magnetic flux tube it comes through. In the Aharonov–Casher effect, the particle has a magnetic moment and the tubes are charged instead. It is used for example to observe interference of neutrons or fluxons.

In both effects the particle acquires some phase shift (${\displaystyle \varphi }$) while traveling along some path P. In the Aharonov–Bohm effect it is

${\displaystyle \varphi _{AB}={\frac {q}{\hbar }}\int _{P}{\mathbf {A} }\cdot d{\mathbf {x} }}$

While for the Aharonov–Casher effect it is

${\displaystyle \varphi _{AC}={\frac {1}{\hbar c^{2}}}\int _{P}({\mathbf {E} }\times {\boldsymbol {\mu }})\cdot d{\mathbf {x} }}$

where ${\displaystyle q}$ is its charge and ${\displaystyle {\boldsymbol {\mu }}}$ is the magnetic moment.

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