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

  • Thread starter anban
  • Start date
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1. The problem statement, all variables and given/known data

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


2. Relevant equations


3. The attempt at a solution\

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.
 
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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.
 
Can you use shell theorem to just treat it as a point charge, as long as the charge is symmetrically distributed?
 
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That would be the result of Gauß' law ;).
 

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