A theoretical question on potential

[mskaroly]

When defining voltage we define it with respect to infinity. However sometimes we also refer it with respect to earth. What is the difference or similarity between these?

When considering the capacitance of a single sphere should we consider earth or infinity as the other plate? What is the difference in these two cases?

[Erikve]

I think this is not the correct place to ask this. But the answer is easy: the potential almost always is defined as the difference between two points. This can be for example between infinty and the edge of your sphere.
The reason why you are puzzled is that there is an altenative way to define potential: the difference between point r (where V=V(r) at point r=(x,y,z)) and the point R (where V(R)=0)

Thus normally Delta V = V(r)-V(R)
but for V(R)=0 -- > Delta V = V(r)

Potentials can be zero in infinity, r=R, r=... etc. So you choose you second boundary R as V(R)=0

For a single sphere you have V(R)=0 for R-->inf.

[berkeman]

This is a fine place to ask, and Erikve's answer is correct.