Findng electric force for line of charge

[lonewolf219]

Homework Statement

Find the force acting on an electron located "d" distance from the midpoint of a line of charge, length "L", located on the x axis. The line of charge is positive.

Homework Equations

F(e)=kq1q2/r^2

The Attempt at a Solution

λ=linear density, here the charge is uniform.
So, dq=λdx I think?
The distance is the variable that is changing, so we should integrate the dx and the limits should be over the length of the line?

k, e(electron) and λ are constant and can be brought out of integral... if the origin is the midpoint, then the limits of integration are -L/2 to L/2? The solution the book gives is the following:

4keλL/(4d^2-L^2)

I don't know where I'm going wrong with this equation, maybe I have the wrong r value?
Is r=(d-x)^2 when dx is along the positive x axis?
Any tips or perspectives would be great!

 

[tiny-tim]

hi lonewolf219!

So, dq=λdx I think?

yes

Is r=(d-x)^2 when dx is along the positive x axis?

how can a distance equal a distance squared?

(and don't forget that force is a vector, so you'll need to integrate the component )

 

[lonewolf219]

Ah, yes, that's why I prefer energy! The electron is also along the x axis, so the angle between the line and the electron is 0, so cos(0)=1?

Using Coulomb's formula, where denominator "r" is squared. The distance between the electron and a dx element of the line (?) can be represented by what? Is it d-x, where we don't know the value of x? Or d+x?

 

[tiny-tim]

Using Coulomb's formula, where denominator "r" is squared. The distance between the electron and a dx element of the line (?) can be represented by what? Is it d-x, where we don't know the value of x? Or d+x?

ah, i think the question means that the electron is on the y axis

The electron is also along the x axis, so the angle between the line and the electron is 0, so cos(0)=1?

see above