## osanseviero one year ago Electric field question

1. osanseviero

There is an electrical field. There is a line with constant density. We know L (how long is the line). At a distance a from the middle, there is a point. Which is the field there? |dw:1441428125288:dw|

2. UnkleRhaukus

is $$L\gg a$$?

3. osanseviero

Yep

4. osanseviero

It is not infinite though, so I don't think we can use Gauss here

5. osanseviero

Actually it does not say anything about the relationship between a and L

6. UnkleRhaukus

i don't know how to deal with the fringing effects the occur at the the end point of the line, i do know how to get the E field if the line if infinite, (good approximation if a<<L)

7. UnkleRhaukus

hmm i maybe if a is a point above the MIDDLE of the line , the fringing effect from both sides cancel

8. osanseviero

It is in the middle

9. osanseviero

So I would guess that in horizontal all of them cancel

10. UnkleRhaukus

|dw:1441430062457:dw|

11. osanseviero

So I would have to use Gauss?

12. UnkleRhaukus

yeah use this cylinder as your gaussian pill box

13. osanseviero

Doing that I have E(2pi*a*L) = Qin / epsilon. But they told me doing this was not correct

14. UnkleRhaukus

is Qin the total charge of the line?

15. UnkleRhaukus

i think you have to express the charge in terms of a linear charge density $$\lambda$$ $\lambda = q/L$

16. osanseviero

E = lambda/(2 * pi * a * Eo) (Eo is the epsilon)

17. osanseviero

But still...how would you solve this without Gauss?

18. UnkleRhaukus

you mean like using Coulombs law?

19. osanseviero

Yep. Coulomb + Electric field

20. osanseviero

And charge distributions

21. osanseviero

Found an answer, thanks a lot