Electric Potential in a Conductor

AI Thread Summary
The discussion revolves around calculating the electric potential, V(r), in a system consisting of a hollow metal spherical shell with charge -q and a solid metal sphere with charge +q at its center. For regions where r < ra, the potential is derived from both the solid sphere and the hollow shell, resulting in V = k[(q/ra) - (q/rb)]. In the region between ra and rb, the potential remains constant due to the shielding effect of the hollow shell. For r > rb, the potential is zero as the contributions from both charges cancel each other out. The confusion arises from the expectation that the potential inside the solid sphere should be constant, while the solution accounts for the contributions from both charge distributions.
saugei
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#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?
 
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what is your understanding of potential, please.(you are online)
 
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