Question

Find the electric field at a distance Z above the center of a circular loop of radius r, which carries a uniform line charge λ.

Answer 1

Recall that r^ depends on θ in the following way:

r^=cosθx^+sinθy^

It follows that

∫2π0r^dθ=x^∫2π0cosθdθ+y^∫2π0sinθdθ=0+0