Integrating an infinite horizontal line charge.
You have in infinite line charge across the x-axis, and you integrate to determine the electric field on a test charge y above the origin. All components of the electric field cancel except for the y-component, so you determine the force and multiply it by cosine theta. I'm having difficulty determining the limits of integration? I think? It seems to me, that if you were to imagine the x-component of this horizontal line charge, -inf would provide an electric field vector with 0 degrees respect to x-axis, and +inf would be 180 degrees. CONT vvv

Question

Integrating an infinite horizontal line charge.
You have in infinite line charge across the x-axis, and you integrate to determine the electric field on a test charge y above the origin. All components of the electric field cancel except for the y-component, so you determine the force and multiply it by cosine theta. I'm having difficulty determining the limits of integration? I think? It seems to me, that if you were to imagine the x-component of this horizontal line charge, -inf would provide an electric field vector with 0 degrees respect to x-axis, and +inf would be 180 degrees. CONT vvv

anonymous · Answer

But when I integrate within those limits, my answer is 0. If I break it into two integrals, I get the right answer. Is this just a formality that I'm missing or something? The reason I'm really confused is because my professor used different limits in class, he integrated from -pi/2 to pi/2 I believe, and I really don't understand that at all.

anonymous · Answer

I forgot to mention, I am integrating with trigonometry. Using coloumbs law, converting everything to constants and cos theta, then the integral ends up being constant*-sin theta, which I'm confused about the limits. If I do 0 to 90 degrees, then 90 degrees to 180, and add the two, I'm fine. But if I do it 0 to 180, I get the wrong answer or zero even. Is this just a consequence of integrating the sin function that I'm just missing?