Re: [Phys-L] amusing electrostatics exercise

[John Denker <jsd@av8n.com>]

On 02/27/2013 08:14 AM, Bruce Sherwood wrote:
> One way to handle this is to consider the superposition of the field of a
> solid wire and the field of a wire the size of the hole, with current
> running in the opposite direction. Ampere's law gives you the field at any
> location for each of these current distributions; add them vectorially.

How do you do that in a way that upholds conservation of charge?
As another way of saying the same thing, how do you make the current 
in the hole become part of a complete circuit?