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I am trying to solve something regarding LINACs:

Assume we have an isolated, hollow, open-ended, thin-walled cylindrical conductor, with a net charge.

The net electric field within the cylinder is ostensibly zero, but since it isn't a closed surface, is there a net electric field near the open boundaries of the cylinder?

I tried to solve it using integral methods, but I ended up having to integrate over a function involving elliptic integrals of the first kind, which is hard, and I'm stupid.