Potential Difference between conductors for a coaxial cable, conflict

[rwooduk]

conflicting results.

find the potential between the two conductors of a coaxial cable



I have already found E... E = lambda / 2 pi r epsilon



my question: What are the integration limits for finding the potential between the conductors?

say we have a radius a (inner conductor) and a radius b (outer conductor). do i integrate between a and b to find the potential between them?

This video says yes...



however if i do that V between the conductors will be CONSTANT i.e the integral will give log of a over b.

This video says no...



in this video he takes the limits between r and b, thus his solution will be a function of r, NOT CONSTANT. then he draws a graph to show it.

SO is the potential between the conducting plates constant (ln (a/b)) or NOT constant (ln (b/r)).

thanks for any help!

 

[TSny]

It all depends on the interpretation of "potential between the two conductors".

If you mean the difference in potential between a point on the inner conductor and a point on the outer conductor, then the answer will be a constant that depends on a and b. If you mean the difference in potential between a point on the inner conductor and an arbitrary point lying between the conductors, then the answer will be a function of the distance r of the arbitrary point from the central axis of the cable.

 

[rwooduk]

hmm the question says

Calculate the total potential difference delta V between the conductors if they were to carry equal and opposite charges +/- Q on the conductors.

since it says between the conductors then I'm assuming it means any point between them so it would be a function of r.

thanks for the help!

edit any idea why in the second video he uses the outer conductor (b) and a point between the conductors as the limits, and not the inner conductor (a) and a point between the conductors as the limits?

 

[TSny]

hmm the question says

Calculate the total potential difference delta V between the conductors if they were to carry equal and opposite charges +/- Q on the conductors.

since it says between the conductors then I'm assuming it means any point between them so it would be a function of r.

Actually, from the wording I think they are likely asking for the difference in potential between points on the the inner conductor and points on the outer conductor. If they wanted V as a function of r, I think they would have asked for the potential at points between the conductors. The phrase "total potential difference between the conductors" seems to me to mean the difference in potential as you go from one conductor to the other. It's similar to picking two points p1 and p2 in space and asking for the potential difference between the two points. That would generally be interpreted as finding V2-V1 where V2 is the potential at p2 and V1 is the potential at p1. That's my opinion, anyway.

any idea why in the second video he uses the outer conductor (b) and a point between the conductors as the limits, and not the inner conductor (a) and a point between the conductors as the limits?

He is starting at infinity where he is taking the potential to be zero and integrating $\small \vec{E}\cdot d \vec{r}$ to find the potential relative to infinity. So, he reaches the outer conductor first and then integrates from there on into the space between the conductors.

 

[rwooduk]

When you put it like that I agree. And I see, thanks for the additional reply!