Determination of signs in basic capacitance problems

[Mr_J]

In my electromagnetics textbook ("Fundamentals of Engineering Electromagnetics" by DK Cheng) there is a typical problem with capacitance, conductors and cylindrical or spherical symmetry which pops up with different variations several times in the problems section of the electrostatics chapter. It goes something like this:

"The radius of the core and the inner radius of the outer conductor of a very long coaxial cable are r_i and r₀, respectively. The space between the conductors is filled with a layer of dielectric with dielectric constant epsilon. Deterimine the capacitance per unit length."

Now, I am able to solve this problem and get an answer which is identical with the one given in the book, but with one exception: my answer frequently has the "wrong" sign.

My question, then, is: is there a "right" or "wrong" sign for the capacitance in the above problem? In my calculations, the sign in the answer changes if I switch the signs for the charges in the two conductors in the cable (in the solution of the problem you can either set the core to charge Q and the outer conductor to -Q -- where Q is positive -- or, you could set the core to -Q and the outer conductor to Q). Is there a way for me to determine what the signs of the charges of the conductors really are? Does it really matter?

 

[vela]

When you calculate the potential difference V, you want to integrate along a path that goes from the negatively charged conductor to the positively charged conductor so that V comes out positive.