Electric field due to point charge in cylindrical co-ordinates

[fengqiu]

I need to use coulombs law to describe the electric field due to a point charge in cylindrical co ordinates. I know the answer should have E = [ρ,0,z] with the azimuth as 0 but I can't show it using the standard electric field equations. please note I need to use E=q/4πε * r/|r|^3 I'm sorry I don't know how to type it all pretty in latex :( it's on my to do list
E=q/4πε * r/|r|^3
I'm truly perplexed on where to start
Thanks for all the help!

 

[BruceW]

hey, welcome to physicsforums :)
well, start writing down the equations you know will be useful. You know the answer in Cartesian coordinates. So then the question is how to get to cylindrical coordinates, from the Cartesian ones. Also, it seems they want you to give an answer in terms of cylindrical unit vectors, so you're going to need to decide what the cylindrical unit vectors are.

 

[fengqiu]

Hi thanks for the help. So say in the simple case i have E=q/4pie0 * r/(|r|^3), so basically i use the unit basis vectors as r/|r| = rhat. now from common sense I know that r = p^2+z^2 but to prove this mathematically...
I think phi(hat) = -xhat * sin(phi) +yhat*cos(phi) which.. makes me stuck haha,
how does this equal 0?

thanks loads BruceW for your help! I feel so nooby, i guess that's what i get from jumping straight back intp physics after an engineering background!

 

[vanhees71]

The field is
$$\vec{E}=\frac{Q}{4 \pi \epsilon_0 r^3} \vec{r},$$
and you can easily rewrite everything in cylinder coordinates, e.g.,
$$\vec{r}=\rho \vec{e}_{\rho} + z \vec{e}_z$$
etc.