A coaxial cable used in a transmission line has an inner radius of 0.14 mm and an outer radius of 0.64 mm. Calculate the capacitance per meter for the cable. Assume that the space between the conductors is filled with a material with a dielectric constant of 2.0.

Question

austinl · Answer

I arrived at an answer of $7.31744\times10^{-11}~pF/m$

Evidently this is wrong...

austinl · Answer

@whpalmer4 do you think you could assist me?

whpalmer4 · Answer

Hmm, E&M was never one of my stronger subjects, and it's been quite a while, but we can try working through it together.  Can you show me how you got what you got?

austinl · Answer

Okay.

$\Large{C=\kappa C_0=\frac{2\pi\kappa\epsilon_0 L}{\ln(b/a)}}$

$\large{C_0=capacitance~w/o~dielectric\
\kappa=dielectric~constant\
L=Length\
a=inner~radius\
b=outer~radius}$

The equation we need.

$\Large{\frac{C}{L}=\frac{2\pi\kappa\epsilon_0}{\ln(b/a)}}$

And just plug and chug.

whpalmer4 · Answer

I come up with $$7.32075*10^{-11} \text{F/m}$$

whpalmer4 · Answer

I think maybe your error is simply a unit error.  That should be $73.2075\text{ pF/m}$

whpalmer4 · Answer

That agrees with what I get using the calculator at http://www.eeweb.com/toolbox/coax