Communities

tag:snake search within a tag
user:xxxx search by author id
score:0.5 posts with 0.5+ score
"snake oil" exact phrase
created:<1w created < 1 week ago
post_type:xxxx type of post
Q&A

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?

+0
−0

Kinetic energy of any particle (who has mass) is $$T=\frac{1}{2} m\ddot{x}^2$$

OP had took potential as potential energy, that was wrong. $$U=-\int \vec F\cdot d\vec l$$ For the case, The force was $$F=\frac{1}{4\pi\epsilon_0} \frac{Qq}{r^2}\hat r$$

So the lagrangian is $$L=\frac{1}{2}m\dot{x}^2-\frac{1}{4\pi\epsilon_0} \frac{Qq}{r}$$ Now you can get a satisfied answer.

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