The radiation detector known as a Geiger counter uses aclosed, hollow, cylindrical tube with an insulated wire along itsaxis. Suppose a Geiger tube, as it's called, has a1.0-{\rm mm}-diameter wire in a tubewith a 25 {\rm mm} inner diameter. The tube isfilled with a low-pressure gas whose dielectric strength is1.0\times 10^6 {\rm{ V/m}}.

What is the maximum potential difference between the wire and thetube?

\Delta V_{\rm max} =___________kV