I have a point charge in a conducting sphere. The charge can be placed anywhere in the sphere & is acted on by the image charge effect & gravity. If the charge touches the side of the sphere within time t it is considered deposited.
The image charge is given by: F(x) = -q divΦ(x)
Φ = - q 1
4πε0r0 1-R2
r0 is the radius of the sphere. r is the radius at which the charge is at. And R= r/ r0
I’m trying to find the volume of the sphere within which the charge will definitely deposit in time t.
I have modelled this situation using excel. Due to symmetry I’m only modelling a quarter of the sphere, (the quarter encompassing the positive & negative z axes, & the positive x & y axis).
In my model I put in the initial position of the charge using x, y & z co-ordinates.
I’m stuck on which initial positions I need to put the charge in in order to find this volume? I know that this should be quite a simple thing to do but I have really confused myself with this!
Thanks
