To calculate the capacitance of the cable per kilometer, you can use the following formula:
C = ε * ε0 * A / d
where:
C is the capacitance of the cable per kilometer (in farads)
ε is the relative permittivity of the insulation (3.5 in this case)
ε0 is the permittivity of free space (8.85 x 10^-12 F/m)
A is the area of the cross-section of the cable (in m^2)
d is the thickness of the insulation (in m)
First, you need to convert the core radius and insulation thickness to meters:
r = 1.25 cm = 0.0125 m
d = 2.13 cm = 0.0213 m
Then, you can use the formula above to calculate the capacitance:
C = (3.5 * 8.85 x 10^-12 F/m) * π * r^2 / 0.0213 m
= 6.44 x 10^-11 F/m
To convert the capacitance to nanofarads per kilometer, you can multiply it by 10^9:
C (nF/km) = 6.44 x 10^-11 F/m * 10^9
= 644 nF/km
So the capacitance of the cable per kilometer would be approximately 644 nanofarads.