A 2 x 10^(-6) C charge is located at A(4,3,5) in free space, find E_rho, E_phi, E_z, at O(8,12,2). (The problem wants the electric field components in cylindrical components).
Since the points are given in Cartesian, I solved the problem in Cartesian coordinates.
E = [2x10^(-6)] / [4 * pi * 8.854 x 10^12 * sqrt^3] [ 4a_x + 9a_y + 3a_z]
E = 65.88a_x + 148.24a_y - 49.41a_z
Since in cylindrical components the z component is the same as the z component in Cartesian, I was able to verify that at least the z component is correct. However, I try to determine E_rho and E_phi and cant seem to get the right answer, which is (159.7 and 27.4 respectively).
I do E_rho = 65.88 cos( arctan( 148.24 / 65.88) ) + 148.24 sin( arctan( 148.24 / 65.88) )
and E_phi = -65.88 sin ( arctan( 148.24 / 65.88) ) + 148.24 cos( arctan( 148.24 / 65.88) )
What am I doing wrong?