If you have a line of charge with charge density [tex]\lambda=\frac{dq}{dl}[/tex] and you want to find the electric field at a perpendicular distance z from the midpoint, you get(adsbygoogle = window.adsbygoogle || []).push({});

[tex]dE = \frac{1}{4\pi\epsilon_0}\frac{\lambda}{r^2}dl[/tex]

Then you integrate [tex]dE[/tex] from one end of the line of charge to the other. (e.g. [tex]\int_{-L}^L ... dl[/tex])

Obviously if you reverse the integral terminals you get the negative of your original answer, butphysically, why should reversing integral terminals even matter? (i.e. [tex]\int_L^{-L}...dl[/tex])

After all, the physical interpretation of the integral is just summing up the little [tex]dq[/tex]s over the line, what does it matter which direction you do it in? And importantly, how do you know which is the correct direction to sum up the [tex]dq[/tex]s?

Thanks

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# Finding the E field direction of integration

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