See figure attached for problem statement, solution provided and my solution.

I'm getting confused about the reference point for the potential.

First find the potential at point z with reference at infinity,

\(\phi(z) - \phi(\infty) = \alpha\)

Now find the potential at point z=0 with reference at infinity,

\(\phi(0) - \phi(\infty) = \beta\)

Now the potential at z with the reference at z=0, which is the same as the voltage difference between the individual voltages at z and z=0 with their reference point at infinity. (Is this statement true?)

\(\alpha - \beta = \phi(z) - \phi(0)\)

The question wants me to solve for,

\(\phi(z)\)

but it seems as though I've given them,

\(\phi(z) - \phi(0)\)

What am I interpreting differently? What am I confusing myself with?

Thanks again!

 

Phi(z=0) = 0 (this is the reference). So the two expresions are the same.