Understanding Coulomb's Law: Particle Acceleration and Energy Exchange Explained

[xaratustra]

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.]

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).

 

[xaratustra]

Great answer! thanks.
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!

 

[Studiot]

Please note that your version of Coulomb's law is incomplete.

You need two charges and the full version refers to the force between the two.

By convention we hold one charge stationery to obtain E. You need a mechanical method to achieve this.

 

[sardar]

I can explain that Coulomb's law is a fundamental principle in electromagnetism that describes the relationship between electric charges. It states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

In the context of particle acceleration, this means that when an electric field is applied to a charged particle, it will experience a force that causes it to accelerate. This acceleration results in a change in the particle's position, which we observe as mechanical displacement.

As for why mechanical displacement occurs rather than a change in the particle's internal energy, it is because electric fields exert forces on the entire particle, not just on individual particles within it. This means that the entire particle will experience a force and move as a whole, rather than experiencing changes in its internal energy levels.

In terms of energy exchange, it is important to understand that both the field and the particle can gain or lose energy from each other. The electric field exerts a force on the charged particle, causing it to accelerate and gain kinetic energy. At the same time, the charged particle also exerts a force on the electric field, causing it to store potential energy.

Overall, Coulomb's law helps us understand the interactions between electric charges and how they can lead to particle acceleration and energy exchange. It is a crucial concept in understanding many phenomena in electromagnetism and has numerous practical applications in modern technology.