Potential on an Uncharged Conducting Sphere Due to a Point Charge I'm working on a problem where I need to find the change in potential of a point on a conducting sphere ("A") a distance 3R from a point charge "q" (R=radius of the sphere).
My confusion stems from the very beginning of the problem and how to initially calculate the potential at point "A". An uncharged conducting sphere will be effectively neutral and the +q charge placed will induce those charges to orient themselves accordingly.
How would one go about setting up this problem; first steps??

 A: If you are looking for the difference in potential from one point to another on the surface of the sphere, the answer is zero.  Since the E field inside a non-driven conductor must be zero, the potential must be the same at all points in and on the conductor.  If you are looking for the change which occurs when you bring the sphere (or the charge q) in from infinity, then you have a very challenging problem. First you have to determine the charge distribution induced on the surface of the sphere which is needed to cancel the field from (q) inside the sphere.  Outside the sphere, the induced charge produces a dipole like field which combines with the field from (q).  Finally you integrate that resultant field in from infinity to get the potential at the sphere.
A: There is this method called the method of image charges.
I'm assuming you are familiar with gausses' law, meaning you know that if the solution you come up with satisfies the conditions (initials or if there are charge densities where you are solving your equations), it can be used as a model to predict values in that scenario.
Having said that, let's loo at this specific scenario. There are certain things that can be seen right of the bat:

*

*No matter how charge is distributed in the sphere, it's always neutral

*E field is perpendicular to the surface of the sphere

so if one intends to find a value outside of the sphere, where we assume no electric charge density is present, the "unique" solution found by guessing would actually work. If the said setup complies with the conditions then it's a unique solution to the situation. let's go about the solution this way:
If the electric field only has a normal component, that means going from point x to point y on the surface of the sphere, it won't take any work, since
$$Work = F.A = |F||A|cos(angle)$$
and the cosine makes the work zero, meaning that all the points on the surface of the sphere have the same potential. (they are called equipotential)
This makes sense since an "ideal" conductor has no electric resistance, thus no change in Voltage/Energy, this is also implied since the no change in voltage also means no electric field (which is a result of change of potentials between 2 points) inside the conductor, which is another assumed characteristic of the perfect conductor.
Just to add a bit more for a some expansion, if you put a charge Q at the center of the sphere, and a -Q at some distance D, the said conditions will apply, making this setup a solution. That can then be used to calculate values in that environment.
