What is the Capacitance and Potential Difference of a Coaxial Cable?

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SUMMARY

The capacitance of a 31 m coaxial cable with a solid cylindrical inner conductor of 2.042 mm diameter and a surrounding cylindrical shell of 6.748 mm inner diameter is calculated using the formula C = L(2πε₀/ln(D/d)). With ε₀ as the permittivity of free space and the Coulomb constant at 8.98755 × 10^9 N·m²/C², the capacitance results in a value expressed in nanofarads (nF). The potential difference between the conductors can be determined using the relationship Q = CU, where Q is the charge of 7.32 μC.

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A 31 m length of coaxial cable has a solid
cylindrical wire inner conductor with a di-
ameter of 2.042 mm and carries a charge of
7.32 μC. The surrounding conductor is a
cylindrical shell and has an inner diameter of
6.748 mm and a charge of −7.32 μC.
Assume the region between the conductors
is air. The Coulomb constant is 8.98755 ×
109 N · m2/C2.
What is the capacitance of this cable? An-
swer in units of nF.

What is the potential difference between the
two conductors? Answer in units of kV

need help, I tried it but failed to get the right answer
 
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[tex]C=L\frac{2\pi \epsilon_0}{\ln \frac D d}[/tex]

D=6.748 mm, d=2.042 mm and L=31m.

Then use:

[tex]Q=CU[/tex]
 

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