# Question on capacitance between two parallel cylinders

We are asked to prove that the capacitance of two infinitely long uniformly charged conductors with coaxial cylindrical surfaces is given by $$$$C= \dfrac{2\pi\epsilon_0L}{\mathrm{ln}\left(\dfrac{b}{a}\right)}$$$$

Now, I was successful in proving the relation but I have a conceptual doubt.

Doubt: If the the inner cylinder was hollow (It was solid in the given problem), would the capacitance be different?

My guess: I guess it won't be different. Because the capacitance depends on the potential between the surfaces and does not care what happens beyond the surfaces.

Is this reasoning correct? If not, please explain where is this logic flawed?