In Ex. 3.2 we assumed that the conducting sphere was grounded (V = 0). But with the addition of a second image charge, the same basic model will handle the case of a sphere at any potential V0 (relative, of course, to infinity). What charge should you use, and where should you put it? Find the force of attraction between a point charge q and a neutral conducting sphere.
Reference example 3.2
A point charge q is situated a distance a from the center of a grounded conducting sphere of radius R (Fig. 3.12). Find the potential outside the sphere.
Reference figure 3.12
Step 1 of 4</p>
We have to find the potential at the outside of the sphere and The force of attraction between charge and neutral conducting sphere..
Step 2 of 4</p>
The sphere is equipotential, so if we place the second charge , the potential increases at the centre of sphere.
The new potential is,
is the permittivity of the medium.
is the radius of the sphere
According to gauss law total charge on the sphere is,