I am trying to solve Laplace's equations in two-dimensions in order obtain the voltage field with specified regions and boundaries. One of the regions in the problem is a half-disk. I wish to specify a voltage on the boundary of that half-disk. I do not think that I know what my problem is, but I suspect that the boundary I am generating for that half-disk is wrong.

Ultimately NDSolveValue appears to work, but does not give a plausible answer. This problem does not require much code. It would be very helpful if someone could examine it and let me know what I am doing wrong.