In the picture given to me, 3/4 of a circle is drawn around the origin. Basically every quadrant but the first. The radius is R and the charge density is λ. It says, find the x-component of the electric field on a point charge at the origin.
I integrate coulomb's law so I get
∫kdq/r^2cos(Θ) where Θ goes from pi/2 to pi, because the bottom two quadrants cancel each other out
Now, the solutions given say to do
dq = λR
why do I replace dq with λR ?? I'm very confused about what I'm doing
if q = λ2piR
shouldn't dq= λ ds where ds goes from 0 to 2piR, so why the heck does that give me the wrong answer, why is it just dq = λR, I don't understand why the charge density can just be multiplied by the radius, what does that give you? Shouldn't it be multiplied by the actual length of that bit, as in λ2piR or however much of the circumfrence is being used?