Physics
posted by Physics .
The inner conductor of a coaxial cable has a radius of 0.900 mm, and the outer conductor's inside radius is 5.00 mm. The space between the conductors is filled with polyethylene, which has a dielectric constant of 2.30 and a dielectric strength of 18E6 V/m. What is the maximum potential difference that this cable can withstand?
no idea what to do...
thought it was
V= 18E6*d/k
but it was wrong...

18*10^6 V/m = 18*10^3 Volts. millimeter
Voltage = integral E dr from inner to outer r
2 pi E r = c constant (Gauss, therefore E is maximum beside the inner radius)
so
E = c/(2 pi r)
V = integral (c/2pi) dr/r
V = (c/2pi) ln(Router/Rinner)
V = (c/2pi) ln (5/.9) = 1.71 c/2 pi
now Emax is at r = .9
Emax = c/(.9*2pi)
c = .9*2pi (18*10^6)
so
V = 1.71 * .9 * 18 * 10^3