# Is a charged particle at rest affected by magnetic field?

It is known that particles such as electrons and protons bear electric charge, but not a magnetic charge. When these particles are at rest, are they somehow affected by magnetic field?

The similar question applies to neutrons: are they affected by electric field?

• Electrons and protons have no "magnetic charge", but they do have magnetic moment. They experiences forces in non-uniform magnetic field. – Siyuan Ren Mar 24 '12 at 7:07

Depends on what how far you are willing to go. If you have a solenoid with a uniform time-varying magnetic field, then an electric field is induced by Faraday's law. It will be a circular field, and will make an electron at rest spiral. So the electron at rest is affected by a time-varying magnetic field, though indirectly--via an induced electric field.

Without considering induced fields: An electron will align its spin with a uniform magnetic field, and if the field is nonuniform, it will move along with it. This is because the electron has a magnetic "spin" or dipole moment,

As far as neutrons are concerned, it depends if they have an electric dipole moment(afaict unknown). But, they can be affected in a similar manner by time-varying nonuniform electric fields, since they also have a magnetic moment.

• Thanks. Hence zero (total) magnetic charge does not mean that particle is not affected by magnetic field. – Murod Abdukhakimov Mar 24 '12 at 8:23
• @MurodAbdukhakimov yep. There's no such thing as a magnetic monopole--with net magnetic charge(well, not experimentally verified yet). Magnetic dipoles exist--these have no net magnetic charge, but can be thought of as pairs of opposing charge. – Manishearth Mar 24 '12 at 8:29

It is not. The force on it goes like $F_{\rm Mag} = q\,{\mathbf v} \times {\mathbf B}$ and so if the velocity ${\mathbf v} = {\mathbf 0}$ the force will vanish.

Neutrons have total electric charge which vanishes. In theory, it could have an electric dipole moment, but this is known experimentally to be quite small and maybe exactly zero.

• There is dipole and higher order multipole moments. Charge is just the monopole electric moment. – Slaviks Mar 23 '12 at 18:57
• @Slaviks Are you speaking of electric or magnetic dipoles and multipoles? – Alan Rominger Mar 23 '12 at 20:56
• The magnetic dipole moment dominates both for protons and neutrons, permament electric dipole moment of neutron is being extensively searched for, see en.wikipedia.org/wiki/Neutron_electric_dipole_moment – Slaviks Mar 23 '12 at 21:10
• You've forgotten that an electron has a magnetic dipole moment, and also you've forgotten induced electric feilds. See my answer below.. – Manishearth Mar 24 '12 at 4:25
• This answer is wrong, it assumes there's no electric field, but a time varying magnetic field implies an electric field, which implies a force on the charged particle. The OP didn't mention anything about B, so we can assume it varies with time to stay in the general case. – AccidentalBismuthTransform Jan 29 '18 at 7:08