Potential of a conducting sphere with charge inside

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The electric potential of a hollow neutral conducting sphere with a charge q placed inside is constant at q/R, regardless of the charge's position within the sphere. This constancy arises because the sphere's surface potential remains unchanged as the charge moves, due to the uniform charge distribution on the sphere's surface. The potential at points outside the sphere is determined by the total charge enclosed, which remains q, leading to the same potential calculation. The discussion highlights the importance of understanding electric fields and potentials in electrostatics, particularly through concepts like Gaussian surfaces. The inquiry emphasizes the relevance of established texts, such as Griffiths' "Intro to Electrodynamics," for deeper insights into these principles.
yarospo
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This is a general question:

What is the electric potential of a hollow neutral conducting sphere with radius R with a charge q placed inside it?
Intuitively I understand that it is the same - q/R, no matter where the charge is placed inside the sphere. Can anyone explain why it is so?

My thoughts: The potential on the surface of a conducting sphere is constant, and it seems implausible that I will be able to change the potential of the sphere just by moving the charge inside, and therefore, I may as well place it in the middle and then the potential is obviously q/R.
 
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Hint: What would you expect the charge distribution to "look like" when you are very far from the sphere? What is the total charge enclosed by a spherical, concentric Gaussian surface of radius r>>R? So, if the potential at r=infinity is zero, what must the potential be at any point outside the sphere?
 
Thanks,

I've found a comprehensive and detailed explanation in Griffiths Intro to Electrodynamics. Should have known it'll be there - got to love that book!
:)
 

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