How do I integrate the electric field of an infinite horizontal line charge at some distance y above the line of charge, using trigonometric substitution? I'm having difficulty defining the limits of integration.

Question

hartnn · Answer

what step are you stuck ?
could you give the the intergal function and limits before any substitution?

anonymous · Answer

Basically, you have an infinite horizontal line of charge from -infinity to +infinity. The test charge is y above the line. The electric field symmetry will cancel the electric field in the x direction, so you will only have the y components left. The integral would be coloumb's constant*charge density constant* 1/(x^2+y^2) dx. I'll post a picture

p0sitr0n · Answer

|dw:1423618828269:dw|
if its something like this, you are searching for a in terms of the length of the rod, x and y. however, this is for finite lengths. For infinite, you should assume a limit approximation is valid.