Potantial +q charge in a notr sphere

[buraqenigma]

There is +q charge in a notr sphere that has a radius R and center is located on the origin.Location of the charge is (0,0,a) (a<R).Calculate the electrostatic potantial of any P(x,y,x) point outsite sphere

2. Homework Equations is poisson equation $$\nabla^{2}u=\rho(x,y,z)$$3. I can't start from any where i need a tip where can i start.

 

[malawi_glenn]

what is "notr" ?

 

[buraqenigma]

what is "notr" ?

notr mean sphere has no charge

 

[Niles]

Assuming the sphere isn't grounded, I guess the situation is just equivalent to a point charge q placed at (0,0,a)?

If that is the case, then we put the origin of our coordinate system at the center of the sphere, so the electric field from our point charge is:

$${\bf{E}} = \frac{q}{{4\pi \varepsilon _0 }}\frac{{\left( {x - a,y,z} \right)}}{{\left( {\left( {x - a} \right)^2 + y^2 + z^2 } \right)^3 }}$$

From this you can find the potential.

 

[buraqenigma]

Yes it's grounded (the word that i'cant rememeber) sphere.Thanks for good starting point Niles .I'll come back with my solution

[ P(x,y,x) must be P(x,y,z) ]

 

[Niles]

If it's grounded, then my attempt is wrong - I assumed that it wasn't grounded.

Since the sphere is grounded, we know that the potential on it's surface is 0. In this case we want to solve Poisson's equation, and from the uniqueness theorem we know that if we can find a solution for the potential V that satisfies the boundary conditions, we are guaranteed that it is the correct solution.

In our case the boundary is that V = 0 when r = R. We can use the method of images for this problem, and in this PDF (page 29) the situation is described: http://www.thphys.may.ie/Notes/electromag/part3.pdf

 

[buraqenigma]

Yes, i know the simplest way is image method ,but we want to find any solution of poisson equation for this problem.And the interesting point of this problem is the q charge is inside grounded sphere (a<R). I have soltion for any charge outside sphere(a>R) but i don't know difference bettween solutions under this cases. Can anybody give me a hint?