Electric field of a sphere in a point A

[not_waving]

My first homework for electrostatics course I'm taking is to find the vector of electric field of a completely hollow sphere (radius r, surface charge density σ in a point A, by integrating the electric field through the whole sphere. I already figured out the electric field of a ring in a point on the axis perpendicular to the plane of the ring and passing through its center and I'm supposed to use that. I basically know how I'm supposed to integrate it but I can't seem to get it to work.

Anybody care to help?

 

[lep11]

I basically know how I'm supposed to integrate it but I can't seem to get it to work.

Why? Show us your work.

 

[not_waving]

Okay, so firstly i know the electric field of a ring anywhere on the z axis (1). I divide the sphere into infinitesimal rings, each occupying dtheta of the sphere, to get (2). Plugging in into electric field equation and integrating I get zero, which is true but only inside the sphere. However, the point I'm calculating the electric field in isn't necessarily in the sphere so it's wrong. I'm not good with LATEX so here's some pictures that outline my thoughts

 

[rude man]

My first homework for electrostatics course I'm taking is to find the vector of electric field of a completely hollow sphere (radius r, surface charge density σ in a point A, by integrating the electric field through the whole sphere. I already figured out the electric field of a ring in a point on the axis perpendicular to the plane of the ring and passing through its center and I'm supposed to use that. I basically know how I'm supposed to integrate it but I can't seem to get it to work.

Anybody care to help?

is A inside or ouside the shell?

 

[not_waving]

is A inside or ouside the shell?

I'm supposed to derive both cases. I'd edit my first post to match the template but I don't know where's the edit button so my attempt at a solution is the second post.

 

[not_waving]

Okay I figured I messed up my integration limits, they should be 0 and pi. Though, I still don't get the desired result.

 

[rude man]

Okay I figured I messed up my integration limits, they should be 0 and pi. Though, I still don't get the desired result.

Since you already know what the axial E field is for a ring, I would suggest the integration is over a distance, not an angle - the distance from the center of each ring to M.