Find the electric field at a distance z above the center of a flat circular disk of radius R
The Attempt at a Solution
My attempt to solve this was take the line integral from the center of the circle to the edge. Then, knowing the circle is symmetrical, multiply it by 2*π*r to get the entire circle. 2πr of my line charges make a circle.
that approach worked when finding the electric field due to a ring. In which case I found the field due to a point charge, and multiplied it by the circumference because 2*π*r of the points made the ring. so 2*π*r of the lines should make the area...
but I am not getting the correct answer. On Chegg, They found the an equation for a ring (with radius dr) and integrated. I definitely see how that approach should work, it is the same idea as mine but in reverse (sort of).
My questions is: is my approach wrong? or am I making a mistake in my work?