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## Homework Statement

Find the Electric field at distance z above the mid point of a length L straight line segment, carrying a non-uniform line charge [itex]\lambda = \frac{1}{C} |x|[/itex] where C is a constant

**2. The attempt at a solution**

I note that the horizontal component cancels out.

Hence

E= 2* [itex]\frac{1}{4\pi\epsilon_{0}}[/itex][itex]\frac{\lambda z}{(z^{2}+x^{2})^{3/2}}[/itex] dx

substitute the equation for [itex]\lambda[/itex] and Integrated from x=0 to 1/2 L

I got the solution as [itex] \vec{E} = \frac{1}{4\pi\epsilon_{0}}\frac{2}{C} (1+\frac{z}{\sqrt{\frac{1}{4} L^{2} + z^{2}}})[/itex]

However, I wanted to check my answer as I know that the line will be like a point charge when z>>L. With the equation I obtain, E becomes a constant value when z>>L.... Which does not make sense... I can't find where did I do wrong too... =(