Electric Potential in a Conductor

[saugei]

#1. We have a hollow metal spherical shell with charge -q and with radius rb
#2. We have a soild metal sphere supported by an insulating stand with charge +q and radius rb
#3. The solid metal sphere is located in the center of the hollow metal spherical shell (aka. #2 is in #1)
The question asks me to calculate the potential, V(r) when:
A. r < ra
B. ra < r < rb
C. r > rb

The solution:

A. k*[(q/ ra)-(q/ rb)] where k= 1/(4*pi*epsilon_0)

C. k*[(q/r)-(q/r)] = 0


What I don’t understand:

A. The electric field in #2 is 0; hence the electric potential should be constant. So, I would think that the potential of r < ra should be V=k*(q/ ra) because it is telling us to find the potential inside of ra which should be a constant throughout the solid sphere. Right? Then how come the answer gives me the sum of the electric potential for #1 and #2??

C. I got totally lost at part C any clue please?

 

[mukundpa]

what is your understanding of potential, please.(you are online)

 

[quicknote]

I would like to clarify a few things about the given scenario before providing a response. Firstly, it is important to note that the electric potential in a conductor is constant throughout the material. This means that the potential inside the solid metal sphere (#2) is the same at all points, regardless of the distance from the center. Therefore, the potential at r < ra would indeed be V=k*(q/ ra) as you mentioned.

Now, moving on to part A of the question - the potential at r < ra. In this case, we have a combination of two conductors - the hollow metal spherical shell (#1) and the solid metal sphere (#2). The potential at any point inside the solid sphere is affected by the charges on both conductors. This is why the solution gives the sum of the potentials due to both charges - k*[(q/ ra)-(q/ rb)]. This is because the potential at a point is the sum of the potentials due to all the charges present at that point.

For part C, we are looking at points outside the solid sphere, i.e. r > rb. In this case, the potential is only affected by the charge on the hollow metal spherical shell (#1). Since the potential at infinity is taken to be 0, the potential at any point outside the sphere would be 0 as well. This is because the potential due to the charge on the shell decreases as we move away from it, and at infinity, it becomes 0.

I hope this clarifies your doubts about the solution. It is important to understand that the potential at a point is affected by all the charges present in its vicinity, not just the ones on a single conductor.