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Coaxial conditions:

i) Central copper conductor of diameter 4.8 cm.

ii) Insulating layer of XPLE of thickness 2.3 cm and relative permittivity k = 2.2.

iii) Conducting lead sheath of thickness 2.9 mm.

iv) Insulating HDPE layer of thickness 5 mm and k = 2.4.

v) Outer coating negligible thickness in contact with soil.

My attempt:

I found the XPLE to have a capacitance of 310.70x10^-12 F/m.

To find the potential I assumed the charge between both conductors would equal 0, thus the charge on the inner conductor = -'ve charge on sheath. Hence I can use Q = CV to find the charge:

[tex] 310.73x10^{-12} * \frac{220}{\sqrt{3}} = 3.95x10^{-5} C [/tex]

Then to find potential between the two I use:

[tex] v = \frac{-Q}{2\pi\epsilon_0\epsilon_r}.ln(b/a)[/tex]

[tex]\Rightarrow v = \frac{-Q}{2\pi * 8.8x10^{-12} * 2.4}.ln(0.0789/0.0739) = -19.5 kV[/tex]

Which implies the potential on the lead sheath = [tex]\frac{220}{\sqrt{3}} kV + -19.5kV = 107.5kV[/tex]

Have I done this right?