# Question on Coulomb law

It is known from the Coulomb's law (F = q E) that if an electric field is applied on a charge, it will accelerate it, i.e. the position of the particle changes macroscopically.

But why mechanical displacement? why not a change in particles internal energy, say for example excitation of an energy level?

What determines who is gaining energy from whom? Field from the particle or particle from field?

many thanks.

Jano L.
Gold Member
But why mechanical displacement?

Mechanical displacement in the presence of charged bodies is just an experimental fact. The definition of electric field is that it is the force acting on charged body.

why not a change in particles internal energy, say for example excitation of an energy level?

There is always such change, when the body is composite (has internal energy). For example, placing small charged ball made from aluminum foil in electric field will cause it to deform, i.e. change its internal energy.

With electron it is difficult to find some evidence that it is composite, or that it has some internal, hidden energy. But if it has some, then it is natural to assume it can change as well.

What determines who is gaining energy from whom? Field from the particle or particle from field?

If particle stands still, there is no interchange of energy.

If the particle moves, it forms a small electric current. In case this current is in direction of electric vector the electric field works and the particle gains energy. In case the current is opposite to the electric vector, the field gains energy from the kinetic energy of the particle (or from other object pushing the particle against E).

I was also checking some books on this. Found also the Gauss's law applied to the energy conservation, which states that the sum of mechanical and field energy in a volume V is reduced as energy is radiated away from that volume.

Now is it correct to think like this: If the particle has no internal structure, the only way to exchange energy with it is to change the particle's mechanical energy which in turn causes its macroscopic displacement?
Same question in other words: is macroscopic movement of a structureless charged particle the only way to decide wether it has gained energy or not after a field has "passed by"?

cheers!