# Accelerating charged body, question

1. Dec 15, 2008

### crx

Is there any other force that is acting upon an accelerating electrically charged large body, in free space? Is Lenz's law applying in this situation? I read somewhere that J.J. Thompson observed that is harder to move an object when is charged than when is neutral. If there is a resistive force present as a reaction, what is the support for that force? thanks!

2. Dec 15, 2008

### Crazy Tosser

If an electrically charged object has more inertial mass than a neutral object then yes, it's harder to move.

Last edited: Dec 16, 2008
3. Dec 16, 2008

### Staff: Mentor

Any other force besides what?

4. Dec 16, 2008

### cesiumfrog

It is that momentum is being transferred to waves/photons of the surrounding EM field.

5. Dec 16, 2008

### crx

Mass is the same. I believe that up to a few hundred of gigavolts potential (in case of negative charges) the gained mass can be neglected.

6. Dec 16, 2008

### crx

besides the accelerating force....

7. Dec 16, 2008

### Staff: Mentor

Then what you're probably looking for is the radiation reaction force. I suppose you might be able to think of it as being exerted by the radiation part of the electromagnetic field that the charge produces (but don't quote me on this).

[added] OK, I take back the second sentence. I should have looked at Griffiths first. It's been a long time since I studied this topic in detail, if I ever did. :uhh:

From a quick scan of section 11.2.3 in Griffiths: Divide an extended object (with a continuous charge distribution) into infinitesimal chunks. If the object is accelerating, in general, the force that chunk A exerts on chunk B is not equal and opposite to the force that chunk B exerts on chunk A. The important factor here is apparently the fact that it takes a finite amount of time for changes to propagate from A to B and vice versa; Griffiths uses the "retarded fields" in his derivation. When you add up the resulting unbalanced forces on all possible pairs of chunks, you get a net force on the object, which is the radiation reaction force. Apparently this force doesn't go to zero when you take the limit as the size of the object approaches zero. The result is the Abraham-Lorentz formula for radiation reaction, which can also be derived by using conservation of energy.

I'm definitely not an expert in this, so don't push me much further on this (and others are welcome to correct me), but at least now you have some keywords and names to search for.

Last edited: Dec 16, 2008
8. Dec 16, 2008

### flatmaster

I find it conceptually difficult to think of the reaction force going into the field. There is another mysterious case in E&M where there is apparently no reaction. The Lorentz force for the force acting on a charged particle in a B field.

F = q VXB

In fact, the posed question is a specific case of this problem. There is a book recently published by one of my professors where he addresses this problem. He is able to satisfy Newton's second law, and thus conserve momentum without putting momentum into the field. If I remeber correctly, I believe the special relativistic corrections come out of his formulation of the field equations.

by Junichiro Fukai

Unfortunately, there are many errors in this first edition

9. Dec 16, 2008

### cesiumfrog

Sure, the Lorentz magnetism force can be reduced to an electric force in the particle's rest frame by noticing relativistic effects to the source of the external field. But here is different in that there is no external field source, so there is nowhere but the field itself for the missing momentum to go.

10. Dec 16, 2008

### crx

I just find out that there is a force called Abraham-Lorentz force caused by the "recoil" of the radiation emitted by a charged particle that "jerks" (check wikipedia) at non relativistic speed.
But...there is a similar phenomena in a solenoid when the self induced magnetic field will oppose to the quick variations of the electric current in the coil. There is no radiation emitted, or can be neglected. This effect is used to smooth ripples in dc current (smoothing reactor). It seems like the magnetic field its freezing in space and will interact with the moving charge that created it. But there is no magnetic field before the charge is getting there?(OK this one is just a relativistic view...). So what is going on? Can this effect appear in the case of a large electrically charged mass?