How to find the electric field coming from a sphere WITHOUT using Gauss' law?

[anban]

Homework Statement

How do I find the electric field at a point above the center of a charged sphere? Assume the sphere is a shell.

Homework Equations

The Attempt at a Solution

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I know there will only be a z component to the electric field, because x and y components will cancel by symmetry. I think the process will have to involve integrating over the surface of the sphere. Where do I start?

More things I know (or think I know):
dq = σdA
The dA terms will point radially from the sphere.

 

[mfb]

I think the process will have to involve integrating over the surface of the sphere. Where do I start?

With a coordinate system, and with an expression for the radial component of the electric field as function of the distance to your charge.
You can use symmetry to reduce the two-dimensional integral to a one-dimensional integral quickly.

 

[Anonymous2258]

Can you use shell theorem to just treat it as a point charge, as long as the charge is symmetrically distributed?

 

[mfb]

That would be the result of Gauß' law ;).