Question

Electric field question

Answer 1

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?

Answer 2

is \(L\gg a\)?

Answer 3

Yep

Answer 4

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

Answer 5

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

Answer 6

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)

Answer 7

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

Answer 8

It is in the middle

Answer 9

So I would guess that in horizontal all of them cancel

Answer 10

So I would have to use Gauss?

Answer 11

yeah use this cylinder as your gaussian pill box

Answer 12

Doing that I have E(2pi*a*L) = Qin / epsilon.

But they told me doing this was not correct

Answer 13

is Qin the total charge of the line?

Answer 14

i think you have to express the charge in terms of a linear charge density \(\lambda\)

\[\lambda = q/L\]

Answer 15

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

Answer 16

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

Answer 17

you mean like using Coulombs law?

Answer 18

Yep. Coulomb + Electric field

Answer 19

And charge distributions

Answer 20

Found an answer, thanks a lot