Electric field on a one dimensional line

[nisse pisse]

Homework Statement

An electric charge Q has been evenly divided over a line with the length L. Calculate the electric field in the field spot X0. X0 > L

Homework Equations

The Attempt at a Solution

E = 0SL(dQ/(4*pi*E0*X0^2))

0SL = the integral over 0 to L >_<

dQ = Q*dx/L , I think...

E = (Q/(4*pi*E0*(X0^2)*L))*0SL(dx)

E = (Q/(4*pi*E0*(X0^2)*L))*L

this is not a correct answer so i wonder where I am failing.


The right answer should be (Q/(4*pi*E0))*(1/(L(X0 - L)) - 1/(L*X0))

 

[m.e.t.a.]

3. The Attempt at a Solution

E = 0SL(dQ/(4*pi*E0*X0^2))

The equation

$$E = \frac{1}{{4\pi {\varepsilon _0}}}\int_0^L {\frac{{dQ}}{{{x_0}^2}}}$$

has an error in it.

dQ = Q*dx/L , I think...

This is correct.

Your first equation just needs a small modification. As it currently stands, your equation has constant "$r$", but $r$ is supposed to be the distance between $dx$ and $x_0$, and the position of $dx$ varies between $0$ and $L$.