Calculating Electric Field at the Midpoint of a Charged Rod

[madah12]

Homework Statement

let say we have a positively charged rod with length L then what is the electrical field at the middle point of the rod

Homework Equations

The Attempt at a Solution

I put the origin at the middle point
so dE=Kdq/r^2, dq = Q/L dx
E= kQ/L integral from -L/2 to L/2 (1/x^2)dx
=-KQ/L[2/L +2/L] =KQ/L (4/L) =-4KQ/L^2

well I expected it to be zero and it wasn't so should it be if so then what did I do wrong?

 

[jhae2.718]

The electric field is defined as $$\mathbf{E} = \displaystyle \lim_{q_0 \to 0} \frac{\mathbf{F}}{q_0}$$.

The r² term in the expression for dE is the distance between some charge element dQ and this test charge q₀. You didn't take this into account in your setup.

 

[madah12]

well my test charge q_0 is at the mid point of the rod and so is my origin so the distance between it and any other charge is x.