A coaxial cable contains a copper wire of radius a surrounded by a material of d

Question

A coaxial cable contains a copper wire of radius a surrounded by a material of dielectric constant k with nner radius b (where b > a) and outer radius c. The dielectric material is surrounded by a copper tube of radius c. Assume the free charge density on the copper wire is Q and the free charge density on the copper Find the potential difference from a to b Find the potential difference from b to c Find the potential difference from a to c. Calculate the capacitance per unit length of the cable.

Explanation / Answer

a] Vab = integral -Edr

= integral 2k Q/r dr

= 2k Q ln (b/a)

= Q ln (b/a) / (2pi e0)

b) again Vbc = integral - Edr

= 2 k Q/(K r) where k is coulombs constant and K is dielectric constant.

= Q ln (c/b) / (2pi Ke0)

c] Vac = Q ln (b/a) / (2pi e0) +  Q ln (c/b) / (2pi Ke0)

d] Capacitance per unit length, C/L = Q/Vac

= 1/[ln (b/a) / (2pi e0) + ln (c/b) / (2pi K e0)]

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