Final answer:
To find the distance between the two parallel wire lines, we need to calculate the capacitance and inductance of the wire line first. Using the given values and formulas, we can solve for the distance between the wires.
Step-by-step explanation:
To find the distance between the two parallel wire lines, we need to calculate the capacitance and inductance of the wire line first. The capacitance is given as 6 pF/m and the inductance is given as 15 H/m. Let's consider a small section of the wire line with a length 'l'. The capacitance of this section can be calculated using the formula C = (ε₀A)/d, where ε₀ is the permittivity of free space (8.85 x 10^-12 F/m), A is the area of the wire, and d is the distance between the wires. The inductance of the section can be calculated using the formula L = μ₀(l/A), where μ₀ is the permeability of free space (4π x 10^-7 H/m) and l is the length of the section.
Solving the above equations simultaneously, we get:
6 x 10^-12 = (8.85 x 10^-12)(πr^2)/d
15 = (4π x 10^-7)(l/(πr^2))
From the first equation, we can solve for 'd' to get:
d = (8.85 x 10^-12)(πr^2)/(6 x 10^-12)
Substituting this value into the second equation, we can solve for 'l' to get:
l = (15 x πr^2)/(4π x 10^-7)
Therefore, the distance between the two parallel wire lines is 'l'.