Find the electric field of a point outside sphere

[Coderhk]

Homework Statement

Find the electric field of a point outside sphere without using Gauss's law. (Do not evaluate the integral)

Homework Equations

Coulomb's Law
Spherical Co-ordinate System

The Attempt at a Solution

I have attached my attempt as a picture but now I am stuck, I don't know how I can express the distance (h )from the point to the differential element in terms of the other variables. From symmetry I know the y component of the electric field will cancel out

 

[BvU]

Mission impossible without a complete problem statement: what kind of sphere ? Imaginary, solid, conducting, grounded ?

 

[Coderhk]

Mission impossible without a complete problem statement: what kind of sphere ? Imaginary, solid, conducting, grounded ?

I believe the question is talking about a shpherical shell like a gaussian enclosed sphere. I figured out that I need to express h in terms of the cos law. Thanks.

 

[BvU]

Conducting ? In which case the method of images might help ...