A single particle is known to have a zero dipole moment but a non-vanishing magnetic dipole moment. We have found that the electric dipole moment points along the velocity direction so it gives zero contribution with the electric field. The magnetic moment of a single charge interacts with its magnetic dipole moment with the magnetic field. And since the electric and magnetic fields are perpendicular to the particle velocity, the electric dipole interaction vanishes.
Dear Arbab,
What do you mean by the orthogonality of the electric and magnetic fields respect to the velocity for a charged particle? That is simple to proof for a photon or an electromagnetic field in general, but no so simple for charged particle. Notice that if you have one electron, for an observer at rest the electric field will be in all directions and without electric dipole because it is assumed no spatial electric distribution. But if you include that it has spin and magnetic dipolar moment associated to it, then you have also magnetic moment at rest whose orthogonality is non sense. There is at least one direction where magnetic moment and electric field must coincide.
Let us now have one inertial observer that sees the electron move at velocity v, the transformation of Lorentz doesn't takes into account the spin transformation and also its dipolar magnetic moment.
According to Biot-Savart the magnetic field due to a moving charge with velocity v is given by B=v X E/c^2 so v.B=0, E.B=0 so the fields due to moving charge are perpendicular to each other.
Dear Arbab,
Biot-Savart law is a classical electrodynamic relation between magnetic field produced by an electric current and it is not the good example for your result.
Let us choose a metallic wire, where the density current J can be assumed with an only direction and you apply Ohm's law with an scalar conductivity, thus you are going to have the velocity parallel to the electric field and magnetic field magnetic field orthogonal to both. Thus in this example of Biot-Savart law you can see that your assumption doesn't works.
But let us take the classical electrodynamics equation of motion, i.e. Lorentz law. In such a case, your expression works when the field of the particle in vacuum is zero. This is only a very special case and no true when you don´t consider the spin or the dipolar magnetic moment associated to one fundamental particle, for instance the electron. The things are much more complex in such a case considering the mass of the spinors.
The electric dipole moment of the electron, owing to my calculations, is given by d=q hbar/(2mc)=3.08 x 10^-32 Cm but does not show in experiment without seeing its interaction energy with the applied electric field. However, this interaction energy is zero and no way to see this directly.
Dear Christian,
The existence of an electron electric dipole moment different of zero implies a violation of both parity P invariance and time reversal T invariance following the Standard Model. And it has not been found experimentally in spead of many accurate experiments. Notice that the dipolar magnetic moment has been experimentally measured with a high accuracy of 7.6 parts in 10-13 in 2006.
Moreover, the absence of the electric dipole moment breaks the electromagnetic duality as well.
Do you refer that the electric dipole has to have a magnetic dipole associated and vice verse?
One different thing is to speak about general electromagnetism and multipolar approximations. And another very different is to refer to those terms in special materials or geometries. For instance, a charged sphere has always electric dipole zero while it can have a magnetic dipole different than zero. Nothing is lost within the general electromagnetism !
Dear Arbab: Historically the electrical interactions are describe with polarity. Experimentally in the domain that I know there are particles with larger mass than the other let say protons or nucleus and electrons. If the hypothesis of exchanges of small grains of mass to describe the interaction is correct (The Wave and the Quantum State) it seems possible to avoid the notion of positive and negative charges. In this approach is it still reasonable to consider a single particle? In a most general consideration to discuss of the space we need at least two objects. Is it useful for your question? Yours Xavier
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