Q&A
Post

# What's the equation of kinetic energy of charged particle?

+1
−1

I was looking for equation of motion. I came up with a solution but it doesn't satisfy me. Cause I was trying to find motion of that particle using Lagrangian. We know that $$W=\int \vec F\cdot d\vec l$$

$W=T$ for some cases and I came up with $T=qV$. In Euler-Lagrange, kinetic energy has velocity as function, in $T=qV$ there's no velocity directly, the equation actually tells me that particle is gaining kinetic energy from potential (more precisely, potential is converting into kinetic). At first sight, I wrote that $T=\frac{1}{2}m\ddot{r}^2$ what if particle is massless(?) so it's not very helpful. Where I took $$L=0.5m\ddot{r}^2-\frac{1}{4\pi\epsilon_0}{q}{r}$$ if I try solve Euler-Lagrange using that Lagrangian then I get $m\ddot{r}=\vec E$. How force is equal to electric field? It totally doesn’t make any sense to me, their dimension doesn't match either. None of these equation satisfy me. what I think that is I got wrong result for taking kinetic energy which doesn’t apply to charged particle. So what's the kinetic energy of charged particle?

Why does this post require moderator attention?
You might want to add some details to your flag.
Why should this post be closed?

# Comments on What's the equation of kinetic energy of charged particle?

What's the kinetic energy of a massless particle?
Canina‭ wrote 10 months ago:

Not a physicist, so I might be completely wrong here, but for your rebuttal of $T=\frac{1}{2}m\ddot{r}^2$, consider: What is the kinetic energy of a massless particle? Does a massless particle have any kinetic energy?

deleted user wrote 10 months ago:

I believe they have. Let's take photon(s), they are massless but moves too fast. And they have kinetic energy for their motion(?).

maybe I can plug in relativistic mass for massless particle (according to some derivation massless particles can have relativistic mass) but I am not going to use that term until I get clear idea of it

celtschk‭ wrote 10 months ago:

deleted userk The formula for kinetic energy you used is only for non-relativistic particles. It definitely cannot be applied to photons. Photons do have kinetic energy (indeed, all of their energy is kinetic energy), but it isn't given by that formula. This community is part of the Codidact network. We have other communities too — take a look!

You can also join us in chat!

Want to advertise this community? Use our templates!

Like what we're doing? Support us!