I have a question about a coaxial power cable equations

Question

A coaxial power cable has a central wire with radius R₁=0.26 centimeters. It is insulated from a surrounding shield with inside radius R₂= 2 centimeters. The maximum voltage the cable can withstand is called the breakdown voltage V of the insulation. V=ER₁ln(R₂ ⁄ R₁) E is the dielectric strength of the insulation. Suppose you needed to reduce the diameter of the cable to half its original size. What would be the dielectric strength of the new insulation material so that the cable would have the same breakdown voltage ( in terms of the original dielectric strength E_o?

Answer 1

When the thickness is doubled, the strength will be slightly less than doubled,

so if the diameter is cut in half, the strength would be more than cut in half (slightly)

I think the new insulation material will have to have twice (or slightly less than twice) the dielectric strength of the old insulation material to have the same breakdown voltage.

I don't certify this answer as being correct but I offer as something to consider.