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I've been having a hard time with this exercise, I did what I could but I highly doubt I got it right since I missed a few lessons :/. Anyway, here it is:

A transmission line consists of two parallel conducting wires of length

l and radius a separated by a distance b (center to center). The left wire is connected to the positive terminal of a generator acquiring a charge +λ [C/m]. Likewise, the right wire is connected

to the negative terminal acquiring a charge −λ [C/m]. The two wires are

completely embedded into a plastic material of dielectric constant εr = 2.1.

Perform the following calculations:

1. Calculate the net electric field for a point between the two wires whose

distance with respect the left wire is r, closer to the right wire.

Calculate the electric field inside each wire. Assume that the distance

between wires is large enough so they do not influence each other.

2. Calculate the potential difference between the two wires.

3. Calculate the capacity per unit of length of the transmission line. Show

that for b >> a this is Cl ≃ (∏ε/ln(b/a)).

Calculate the numerical value if b = 4 mm and a = 0.7 mm.

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1. What I tried to do in the first one is to calculate the total electric field created by the wires:

Et = Ea + Eb, being a the left wire and b the right one, using vectors of course. This is my result:

Et = (1/(4πε))*((Qa/r^2)+(Qb/(b-r)^2)). I doubt that it's that easy.

2. Here all I could come up with is ΔV = -∫E dr = -E(b-a).

3. I used C = (2∏εL)/(ln(b/a)) = (2∏*2.1*(8.85*10^-12)*L)/(ln(0.004/0.0007) = 6.7*10^-11 Farads per unit length. About the second part for for b >> a I am completely clueless.

Thanks a lot!