# Energy supplied by a force

1. Apr 9, 2005

### El Hombre Invisible

Hi. I'm doing a Physics degree at the moment, and all textbooks seem to talk about work done by a force judged either by the displacement of an object (W = Fs), or its change in velocity (W = /\Etrans). In both cases, the energy given is kind of after the event. Search as I may, I cannot find an equation for the energy supplied by a force.

For instance, two particles of equal mass, one with charge the other neutral, have the same force acting on them. The neutral particle will undergo a change in velocity and possibly potential energy. The charged particle though will also radiate EM energy. This energy must come from somewhere: either its kinetic energy, which would seem to increase its inertia and make it appear more massive; its mass energy, which would lead to a decrease in inertia leading to further acceleration leading to further EM radiation etc, or the energy supplied by the force. With the first two leading to paradoxes, I assume the third is true. Can anyone point me in the right direction? A classical mechanics answer would be preferred, but I'll take what I can get.

2. Apr 9, 2005

### James R

Hmm... or does the energy come from the energy density of the electric field itself?

3. Apr 10, 2005

### El Hombre Invisible

Lemme see if I can get this straight... when a charge is at rest it has an electrostatic field, when moving with constant velocity it has a magnetostatic field and a dynamic electric field, and when accelerated has both dynamic electric and magnetic fields? From your answer, then, the energy of the electrostatic field at any given time is the same as that of the electric and magnetic fields plus that in all electromagnetic waves at any other given time after during acceleration..?

How is this accounted for from a QED PoV cos I thought the photon was emitted from the charged particle itself? In other words, what supplies the energy of an emitted photon?

4. Apr 10, 2005

### pack_rat2

Since a force, by itself, isn't work/energy, I'm not sure what what you're asking, HOWEVER...in the example you give, I'd say that the energy radiated by the charged particle as it decelerates comes from its decrease in kinetic energy. Be aware that I don't know a whole lot about modern physics.

5. Apr 10, 2005

### Andrew Mason

The thing that you are overlooking here is that if the charged particle radiates, there is a force of radiation resistance opposing the applied force (eg. radio antenna). So the charged particle has less acceleration and therefore less kinetic energy than the uncharged particle.

AM

6. Apr 13, 2005

### Kirk Gregory Czuhai

i believe you are making things a lot harder because you are trying too hard!
forget about special and my God do not consider General relativistic relativity right now!
let's just consider classical mechanics and simple classical electical dynamics.
the neutral charge has mass and is acted upon by a force but not an electric force.
when accelerated, unless its accelerated to a velecity at least the velocity about a tenth the velocity of light relativistic effects can probably be ignored and the gain in kinetic energy by the particle will be (1/2)*v^2,
otherwise,
its energy is always E=m * c^2 where m =[m0*(1-v^2/c2) where m0 is its rest mass.

if the mass is charged it will radiate eletromagnetic energy dependent on how it is accelerated as well so,

the work done by the force will be

W=F*D + E,r=(1/2)*v^2 + radiated energy

love and peace,
and,
peace and love,
(kirk) kirk gregory czuhai
http://www.altelco.net/~lovekgc/kirksresume.htm

7. Apr 13, 2005

### Kirk Gregory Czuhai

8. Apr 30, 2005

### El Hombre Invisible

Okay, so we have two votes for a decrease in kinetic energy, so that to me would suggest that a charged particle would appear to have more inertia than it actually does, right? I mean, if accelerating means it must radiate, and radiating means it must slow down, then by F = ma, the particle would appear more massive. Two votes for potential energy, but while I could understand that if the potential energy was decreasing, what if the particle is being accelerated such that its potential energy is increasing, say an electron further and further from a proton? Where does the energy come from to increase the potential energy and still have enough to radiate away? I expect my accelerating force to cause less acceleration thanks to the nearby proton, but would I expect it to cause even less due to radiation?

9. Jun 26, 2006

### Irresistible_Force

If you are asking where does the energy of the fields come from in the first place...then you are on the right track.

No one will tell you.

Keep looking.
As shall I.

10. Jun 26, 2006

### masudr

The definition of how a force does work on a particle (thus increasing it's energy) is easy:

$$W=\int dW = \int \vec{F}\cdot\vec{ds}$$

where $\vec{F}$ is the vector sum of all the forces acting on the particle and $\vec{ds}$ is the vector sum of all the infinitesimal displacements the particle is going through.

As for your question of the energy supplied instantaneously by a force, it is simply:

$$dW=\vec{F}\cdot\vec{ds}$$

Now to your particular example; by the way the question is phrased, we appear to be in the non-relativistic domain, so we can ignore all that stuff for now.

Firstly, may I ask what the purpose of the neutral particle is? When you say they both feel the same force, do you mean equal and opposite? And is this force perhaps gravity acting between the two particles?

If some external agent is supplying the force, and there is no interaction between the two particles, then the EM radiation will result from the energy input by the external agent and the energy change in the EM field. The reason for the radiation is that we must be conserving energy and momentum (and bear in mind that even classical EM radiation carries energy and momentum).

If instead we have gravity doing the moving, then we will have the energy changes in the EM and the Newtonian gravitational field that provide energy for the EM radiation.

So, in summary, (and as far as I know), your initial guess was correct.

11. Jun 26, 2006

### lalbatros

Hi ,

This is not so much the problem, I think. If you spin up a dynamo the torque you need to exert depends on the use made for the energy. If a light bulb is wired to the dynamo it will need a larger torque than if nothing is connected. And, by the way, the end result is radiation too. Clearly, accelerating a charge cost you the radiation as well as the increase in kinetic energy. The "reaction force" on a charged particle is developed in many textbooks and it involves the derivative of the acceleration in first approximation.

However, you are pointing here to an old and fundamental question in electrodynamics.
This is the famous "radiation reaction". Look at this web page for example:

Also look at the names in the references!
I don't know the end of this story. Does anyone know it?

Michel

PS

This is not totally true, since the charged particle is coupled to the electromagnetic field.
The end result, the "radiation reaction", is that the charged particle looses a part of its acceleration to produce the radiation. Just similar to a dynamo, except that the coupling to the field is a more fundamental question.

Last edited: Jun 26, 2006
12. Jun 26, 2006

### Farsight

Somebody tell me again: where does mass come from?

13. Jun 26, 2006

### masudr

What do you actually mean by that question?

The simplest answer is that all particles (or you can go for a continuous distribution of matter and densities) have certain properties that define their characteristics and have subsequent effects on how they behave; these can be measured experimentally. Mass is one such thing.

14. Jun 26, 2006

### Farsight

What I mean is:

Is the thing we call mass the product of a coupling between a property of an object and a property of space? In other words, is there a link between the "radiation reaction" of a charged particle and the inertia of a non-charged particle?