Electric Field of Linear Charge along a Line Segment

[phy6]

Homework Statement

Consider a straight line segment of 3L and with a linear charge density λ. Determine the electric field, E, of at point P, which is a point within the segment and along the axis. (figure attached)

Homework Equations

dE=kdQ/r^2

The Attempt at a Solution

I attempted solving it but I am stuck at the integration part because i don't know from and up to where to integrate it.

 

[scottdave]

I have some trouble matching your picture to the wording in the problem statement. The wording suggests that the point P lies "within" the 3L segment (distance L from the end perhaps?). The picture shows point P at the end of the 3L segment, then another segment L adjacent to that.
As far as your integration, note that your charge density lambda, is actually dQ/dL, with dL representing "delta Length". So you could say that dQ = (lambda)*dL and integrate lengths. Note that the distance r is also a length from the charge to a point. Take care to note how charges on opposite sides of the point will interact to form the resulting electric field (which is a vector).

 

[haruspex]

your charge density lambda, is actually dQ/dL

I advise against such a notation. L is related to the overall length, a constant. An infinitesimal should represent a small change in a variable. Let x be the distance from one end of an element length dx, etc.

@phy6, if you follow the obvious path you will get two improper integrals that do not converge. Think how you might cancel out the infinities by practical considerations first.