# Is the Electric field a well defined concept ?

krab said:
This conclusion is correct.

I might also say that there are very practical consequences of your conclusion. Example: A stream of charged particles from a particle accelerator can be controlled (steered, focused) by electric fields. Such fields are set up by applying voltages to conductors of required shape (parallel plates for steerers, hyperbolic plates for focusing, etc.) For a low current charged particle beam (say less than about a nanoampere), the fields calculated from the voltages and the shapes are sufficient to find the effect on the particles. However, for milliamperes, it is necessary to take into account that the charged particle beam disrupts the charge distributions on the conducting surfaces. This is the same as saying that there are "image charges" that act back on the particle beam.

Not to mention that the very other charges of the flying set of charges (which characterizes the current) may interfere in the dynamics of the "who feels the field" charged particle.

krab
Yes. I didn't want to complicate the picture, but the effect of the flying charges on each other is called the "direct space charge effect", and it is in fact much stronger than the image charge effect until the particle velocities are close to the speed of light.. Non-relativistically, the ratio of the effects is about equal to the square of ((distance of particles to conducting surface) / (radius of particle beam)).

thank you all for the contributions.

Best Regards

DaTario

DaTario said:
Some specific spatial configuration of the E-field is something that has a well definite shape, but exists as long as it is surrounded by "who suffers" charges small enough to label them as: charges approaching zero. Is it?
The field is defined such that it exists without there being test charges. The field is defined such that if a test charge is placed in the field at a given point then it will experience a force per unit charge E = F/q.

Pete

pmb_phy said:
The field is defined such that it exists without there being test charges. The field is defined such that if a test charge is placed in the field at a given point then it will experience a force per unit charge E = F/q.

Pete

But rigorously it is not true, for every test charge will disturb the charge configuration a certain amount and so the field at its location will not anymore be the same.
I must tell you that I am ok with this question already.

Thanks

DaTario