Potential of Shell, Direct integration problems

[physapple89]

Homework Statement

Okay I'm really scratching my brain out here, I've done this a thousand times but aparantly NOT the correct way, here's the problem

A conducting spherical shell of radius R is charged uniformly with total charge Q. By DIRECT integration, find the potential at an arbitrary point r with A)r<R and B)r>R

Homework Equations

V=Q/(4*pi*epsilon*r)

someone also showed me

The Attempt at a Solution

I started out by noting that inside the sphere for any gaussian surface you can draw the total charge density will be 0 and therefore the E field will be 0, and because of that the Voltage will be constant which turns the integral for voltage into two parts

Integration then yields typical results, which while correct, are utterly wrong for the purposes of this question, as it is asking for DIRECT integration, Can anyone help, this isn't making any sense?

 

[tiny-tim]

welcome to pf!

hi physapple89! welcome to pf!

divide the spherical shell into slices perpendicular to the line joining the point to the centre of the shell …

(so all points on the same slice will be at the same distance)

integrate over all the slices …

what do you get? ​

 

[physapple89]

I think that's the part I'm not getting how to do.

 

[tiny-tim]

ok, show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[physapple89]

What I tried was up there, using gauss's law but it didn't quite work, then I tried integrating over the area of the shpere times the surface charge density and that didn't work. I don't think I'm setting this up right.

Basically I need help solving for the dQ so that I can integrate.

 

[physapple89]

is this the correct integral?

basically integrating over the sphere times surface charge density and plugging that into the previous equation.

 

[physapple89]

http://www.kwantlen.bc.ca/science/physics/faculty/mcoombes/P2420_Solutions/VfromCharge/P2420_09_Solutions.htm

does this explain what I'm trying to find, can anyone tell mehow they got dA?

 

[tiny-tim]

i don't understand how you calculated √(r²R² - 2rRcosθ)

"A" comes from 2π times the radius of a "circle of latitude"

start again ​