# Where does energy from changing electric fields go when moving a neutrally charged particle vs a charged particle

I am in the process of trying to understand EM waves. Although I have started studying physics to better understand EM waves most of my knowledge is still centered around electronics so I don't know that much.

Here is my question:

Say a charged particle is moved to one position and then back to it's original position. This will cause a change in its electric field and the energy from that change can then be absorbed.

Now if a neutral particle of the same mass is moved in the same way, no change in any electric field will happen because it is neutral, but because it is of the same mass it should take the same amount of energy to move, right?

This would mean it takes x energy to move each particle individually but an additional amount of energy can be absorbed by the change in the electric field of the charged particle.

So if the total energy to move the particle is x (input energy), if e is the energy radiated through the electric field and o is all other energy transferred then x = o + e. But because e is zero for neutral particles o must be the same as the input energy. So where does the energy go if not transferred through changes in electric fields?

Sorry if this question is flawed/too broad but hopefully this is enough to present the problem in my understanding.

• The extra energy is radiated as the change in the electric field propagates outward. The diagram I wanted to include in an answer is explained at this related question.
– rob
Commented Jul 8, 2023 at 21:43
• Thank you, but the extra energy I am referring to IS the change in electric field. If an amount of energy is used to move 2 particles with the same mass individually, I don't understand where the extra energy from charged particle comes from. Does the charged particle take more energy to move than the neutral even if they have the same mass? I have tried to clarify my question. Commented Jul 8, 2023 at 22:14

I think the mistake in your reasoning is in thinking that it takes the same amount of energy to move the charged particle as it does for the neutral one (assuming you want to give both of them the same acceleration).

This is not true, it actually takes more energy to accelerate the charged one, since part of the energy you give it is irradiated away as soon as it starts moving. So the charged particle will feel harder to move, because you will need to transfer more energy to it to compensate for the loss to the electromagnetic field. The ''additional'' resistance force you will feel when trying to push this charged particle is called the radiation damping force, or Abraham-Lorentz force, and it does not depend at all on the mass, only on the charge. For a point particle moving at speeds much lower than the speed of light, it is given in SI units by $$$$\mathbf{F} = \frac{2}{3} \frac{q^2}{4 \pi \epsilon_0 c^3 } \frac{d \mathbf{a}}{dt},$$$$ where $$\mathbf{a}$$ is the acceleration vector of the particle.

• That makes a lot of sense now, thanks. Commented Jul 9, 2023 at 2:03
• Would it be correct to say the resistance force is caused by the charged particle's own electric field before the change has propagated? Commented Jul 9, 2023 at 8:29
• Maybe, if are referring to the whole backreaction discussion. Understanding this force is one of the trickiest parts of classical electrodynamics, and many people believe this can only be truly resolved by going to quantum electrodynamics. There are many questions here that go into this in more detail. I only mentioned the Abraham-Lorentz force because it makes the fact that the charged particle is harder to move very intuitive. If you only want to discuss where the energy goes, you can do so with the Larmor formula, which is a better understood result. Commented Jul 9, 2023 at 16:17

a charged particle is moved to one position and then back to it's original position. This will cause a change in its electric field and the energy from that change can then be absorbed.

You gain energy when you separate charges. To do this, you have to expend energy. The electrical generator is such a device. Electrons are moved in conductors with the help of rotating magnetic fields. Electrical devices then convert this energy back into light, movement and above all heat.

Of course, you can also use the kinetic energy of the electron directly. This is done in electron beam welding, where a beam of electrons is used in a vacuum chamber to weld together railway tracks, for example.

The kinetic energy you can convert depends on the mass and the final velocity of the body. For the electron beam, this is the total mass of the electrons and their velocity at impact. This also applies to a neutron beam. Or to all the little balls that you let hit the surface.