Electric field of a linear charge on the axis of the line segment

[MyAmpsGoTo11]

Homework Statement

A uniform line charge of linear charge density 5 nC/m extends from x = 0 m to x = 4 m. Find the electric field at x = 7 m. Answer in units of N/C.

Homework Equations

8.85 × 10^−12 C2/(N · m^2) is the permittivity constant
8.98755 ×10^9 (N · m^2)/C^2 is Coulomb's constant
Gauss's Law surface integral of E da = Q/(permittivity constant)

The Attempt at a Solution

I know the field of of a point on the SIDE of the same line segment is
kQ
(r square root of (r^2 +(L/2)^2))
Where r is the distance from the rod, and L the length of the rod, but my attempts are wrong.
I do not know how to find the field of a rod on the same axis.

 

[kuruman]

Hi MyAmpsGoTo11, welcome to PF. Gauss's law is irrelevant here. You need to find a general expression for the electric filed on the axis, then plug in the numbers. To do this, consider the rod as consisting of many small individual point charges dq, find the contribution dE to the electric field at the point of interest of just this charge, then add all such contributions, i.e. integrate over the length of the rod.

 

[MyAmpsGoTo11]

Ah! Awesome. I see. This online homework my teacher assigned is titled Gauss's Law, and I'm disappointed I didn't get it sooner. Thank you so much. :)