Question

a 1.0 cm diameter conductor is sheathed with a 0.5cm thickness of teflon and then a 2.0cm (inner) diameter outer conductor. (a) use laplace's equation to find an expression for the potential as a function of p in the dielectric. (b) find e as a function of p. (c) what is the maximum potential difference that can be applied across this coaxial cable without breaking down the dielectric?

Answer 1

The maximum potential difference that can be applied across this coaxial cable without breaking down the dielectric is 600 V.

(a) The potential as a function of p in the dielectric is given by:

V(p) = V0 * ln(p / a) / ln(b / a)

where:

V0 is the potential difference between the inner and outer conductors

p is the distance from the center of the cable

a is the radius of the inner conductor

b is the radius of the outer conductor

(b) The electric field as a function of p in the dielectric is given by:

E(p) = V0 / (ln(b / a) * p)

(c) The maximum potential difference that can be applied across the cable without breaking down the dielectric is:

Vmax = Emax * (b - a)

where:

Emax is the breakdown strength of the dielectric

Plugging in the values for Teflon, we get:

Vmax = 3e4 V/m * (0.02 m) = 600 V .