Capacitor has no magnetic field, Why?

Ruptor

We know that magnetic fields are generated by moving electrons so there is a magnetic field between the plates of a capacitor due to the displacement current when it charges up. I don't understand why there is no magnetic field on the plate of a capacitor when it is fully charged because electrons are supposed to have a magnetic moment or field of their own and I would have thought that the increased density of electrons on the capacitor plate would exhibit a magnetic field.

mikeph

where is there a net current on a charged capacitor?

HallsofIvy

Where did you get that idea? You just said that magnetic fields are generated by moving electrons. Electrons that are not moving do not have a magnetic field.

Ruptor

The electron has a magnetic field as well as angular momentum so they say here
http://hyperphysics.phy-astr.gsu.edu/hbase/spin.html
So even though electrons don't move through space they have a field like a mini magnet so why doesn't a cloud of electrons give a magnetic field? Perhaps because they are inhomogenous?

dipole

Yes electrons do have an intrinsic magnetic dipole moment, because they have spin 1/2. This is the whole premise behind the Stern-Gerlach experiment, and one of the fundamental building blocks of quantum mechanics.

The reason a charge distribution (whether electrons on a capacitor plate, or along a wire or whatever) doesn't have an associated magnetic field is because the electron spins are randomly orientated, and the contribution of their magnetic fields sum to zero.

Darwin123

There is no time averaged magnetic field on a fully charged capacitor. The direction of the magnetic moments of electrons is random. The magnetic fields caused by "individual electrons" add up linearly at every point within the capacitor. The total magnetic field at any one point adds up to zero vector, or to a fluctuating magnetic field very close to a zero vector.

There are transient magnetic fields in a capacitor on an atomic time scale caused by thermal fluctuations and quantum fluctuations. However, they are generally too small to be significant.

In terms of practical electronics, one can say that part of the "noise" on a circuit is due to random fluctuations in the velocity and spin orientation of each electron. Shot noise is caused by electric currents caused by "quantum fluctuations" in individual electrons. Thermal noise is also caused by the "classical fluctuations" in individual electrons. These sources of noise are have to be modeled using statistics.