For a cylinder of zero thickness, you are correct. The trick is to have nonzero thickness.
Imagine a long cylinder cut into segments. Instead of moving along the line, you merely have to take the segment at one end and move it over to the other end. Because of the superposition principle, the change in potential is merely the change cause by moving the segment from one end to the other.
Now, when does moving the segment increase the potential, and when does moving the segment decrease the potential? Can we identify a maximum?
when does moving the segment increase the potential, and when does moving the segment decrease the potential?
That’s a good approach. If the segment is closer to the point of interest after it is moved, the potential well is deeper. Which tells you that it is deepest at the center.
Imagine a long cylinder cut into segments. Instead of moving along the line, you merely have to take the segment at one end and move it over to the other end. Because of the superposition principle, the change in potential is merely the change cause by moving the segment from one end to the other.
Now, when does moving the segment increase the potential, and when does moving the segment decrease the potential? Can we identify a maximum?
That’s a good approach. If the segment is closer to the point of interest after it is moved, the potential well is deeper. Which tells you that it is deepest at the center.
I sit corrected; my argument that as you enter the cylinder you can ignore the outer parts breaks down.