Describing Coulombian Attraction/Repulsion Using Fields

[DaTario]

Hi All

Does anybody know if there is some formalism according to which we can describe the coulobian repulsion (or attraction) of two point like bodies by just working with its fields.

Notice that in general we are given one particle and one field to solve typically this problem.

Thank you

DaTario

 

[DaTario]

I guess (just now) that minimizing the energy of the superimposed fields of the two particles may lead to the dynamics I am searching for, but I am not 100% sure. I see no mass participation in this approach...

Thanks anyway

DaTario

 

[Defennder]

Um, you have $$\mathbf{F} = q\mathbf{E}$$, so isn't the repulsive/attractive force already determined by the magnitude and direction of the E-fields?

 

[DaTario]

Um, you have $$\mathbf{F} = q\mathbf{E}$$, so isn't the repulsive/attractive force already determined by the magnitude and direction of the E-fields?

I guess I was not clear enough.
My point is the following:

Given just two fields, namely:
a) field 1 which is the field of the particle 1, in position 1 at time t=0, which has the mass 1 and the charge 1 (1 is label here) and

b) field 2 which is the field of particle 2, in position 2 at time t =0, having the mass 2 and charge 2,

by just manupulating these two fields (the masses will have to enter in some place..) the dynamics must follow with the field representation, in the sense that we must have a resultant field, that is a function of time, and which represent the field composed by the sum of particle's field located at positions corresponding to the dynamically correct postions in such a coulombian situation like this.

I expect to have made myself clear, but may be I haven't.

Anyway, thank you.

DaTario

 

[turin]

Does anybody know if there is some formalism according to which we can describe the coulobian repulsion (or attraction) of two point like bodies by just working with its fields.

Indeed. See, for example, Section 1.11 in the third edition of J. D. Jackson's Classical Electrodynamics.

 

[snapback]

Hi All

Does anybody know if there is some formalism according to which we can describe the coulobian repulsion (or attraction) of two point like bodies by just working with its fields.

Notice that in general we are given one particle and one field to solve typically this problem.

Thank you

DaTario

Hi DaTario,

just to be clear that I understand your question. You are looking for a formalism for dynamics of charges which is not relying on the established concept of E and B Fields but arising from the fact the same/opposite charges repulse/attract each other ?

Rgds, snapback

 

[Meir Achuz]

1. You can integrate E_1.E_2 over all space to get the potential energy U.
The3n F=-grad U.
2. You can use the .Maxwell stresws tensor.
Each of these methods is in textbooks.

 

[DaTario]

I guess the way pointed out by clem is the one I was suspecting to be The One.

Thank you all

Best Regards

DaTario

 

[DaTario]

Hi clem, I am giving a step back on what I have said. What is E_1 and E_2 in your proposal?

I am looking for a formalism that from two particles fields and from their masses, one receive at the end two vectorial fields which depend on time and reflect the attraction or repulsion of the respective point charges.

best regards

DaTario

 

[Meir Achuz]

E1 and E2 are the electric fields you described:
"a) field 1 which is the field of the particle 1, in position 1 at time t=0, which has the mass 1 and the charge 1 (1 is label here) and

b) field 2 which is the field of particle 2, in position 2 at time t =0, having the mass 2 and charge 2,"

However, finding the force by the two methods I gave in post #7 works only in the static case. If either charge is in motion, the force becomes very complicated because of the retarded time.

 

[DaTario]

I agree with you. But anyway I saw no reference in which one starts from two point like fields of positive charges, for instance, and applying a given formalism ends up with a time dependent field which is the superposition of two point like fields getting far from each other.

There must also be place for magnetism (which will be for certain in Maxwell tensor).

Best wishes

DaTario

 

[dE_logics]

You mean a particle submersed in a field.

Yes, all you should know is a function to give you the right intensity of the E.F in space, then you can calculate the force on the charge.