Capacitance in a Cylinder: Which Direction is the Voltage Calculated?

[sebby_man]

Hi everyone

In most problems I've seen involving capacitance of a coaxial cable, there is an inner cylinder of radius a with +Q charge and and an outer cylinder of radius b with -Q charge. The voltage is calculated from a to b. However, in this problem the inner cylinder is -Q and the outer is +Q. In this case, would I still find the voltage from a to b, or would I find the voltage from b to a? The answer key suggests that the voltage is calculated from a to b, but I'm not sure why.

 

[free-thinker]

Hi,

You should calculate the voltage in that way that produces a positive voltage. The cause is capacitance always is a positive number. If the inner cylinder has -Q charge, the integral for voltage should be made from b to a.

I apologize for my english. I hope this can be clear for you.

 

[sebby_man]

Ok, so if I'm finding the voltage from b to a, then I need to calculate the integral of E dr from a to b? The answer of the integral is then [q/(2*pi*height*epsilon_0)]*ln(a/b). This seems right to me (unless I've made some simple mistake inbetween), yet the book says it should be ln(b/a) instead.

 

[Gordianus]

ln (a/b)=-ln(b/a)

It´s only a matter of sign

 

[sebby_man]

Turns out I had made a simple mistake in my calculations. Instead of [q/(2*pi*height*epsilon_0)]*ln(a/b) I should have written [-q/(2*pi*height*epsilon_0)]*ln(a/b) because the charge of the inner cylinder is negative. Thanks for helping me realize my careless mistake.