Question

A coaxial cable consists of a solid inner conductor of radius R(sub 1) surrounded by a concentric cylindrical tube of inner radius R(sub 2) and outer radius R(sub 3). The conductors carry equal and opposite currents I(sub 0) distributed uniformly across their cross sections. (See photo for my question)

Answer 1

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Answer 2

this all looks wrong/ messed up, to me. Gaussian surface? you are looking at Ampere's Law and Amperian loops.

the question starts by asking for the mag field at r > r3; but the solution seems to look at region r2 < r < r3 . and then it messes up the calculation.

if you can figure out what you need to find, it should be pretty straightforward.

Answer 3

My mistake. The question should have been "Determine the magnetic field at a distance R from the axis for \[R _{2}<R<R_{3}\]."

Other than that, everything was just taken from a solution online.

Answer 4

its because they are netting off the field due to the current in the inner wire:

\[I_o = I_o \frac{r_3^2 - r_2^2}{r_3^2 - r_2^2}\]

yes?

Answer 5

That's the answer, yes, but I'm still confused. How did the numerator's subscripts for r, turn into the one that you mentioned above?

Answer 6

R became \[R_{3}\] and \[R_{2}\] became R .

Answer 7

\[I_{net} = I_o - I_o \frac{r ^2 - r_2 ^2}{r_3 ^2 - r_2 ^2} = I_o[ \frac{r_3 ^2 - r_2 ^2}{r_3 ^2 - r_2 ^2} - \frac{r ^2 - r_2 ^2}{r_3 ^2 - r_2 ^2} ] = I_o \frac{r_3 ^2 - r ^2}{r_3 ^2 - r_2 ^2}\]

Answer 8

Thanks. Although is there anything else left that you can add to the explanation? I guess I'm just asking for a method that would enable me to "see it" clearly, because I'll admit that I'm still not completely understanding it. Was it derived from the equation J = I*A which is the current density?

Another more specific question: Why is it that "r3 - r" = "r"? Shouldn't it be "r2"?

Answer 9

you mean the numerator ? like this [i'll leave out the squares]:
(r3 - r2) - (r - r2) = r3 - r2 - r - (- r2) =
r3 - r2 - r + r2 =
r3 - r

and, yes, it all follows from Ampere's Law, Maxwell's 4th equation [really Oliver Heaviside's 4th!!] equation. i still haven't figured out how to do vector symbols in latex or i'd post the formula.

if you are studying Ampere's law, or anything to do with electricity/ magnetism or Maxwell's laws for that matter, then there is a guy on Youtube -- lasseviren1 -- who covers all the basics with awesome clarity.

this is his first vid on Ampere's Law:
https://www.youtube.com/watch?v=ryGzpGpTtIM&index=6&list=PL8CE51E84F067070E

look at the rest of this particular series on the right side of this page, and maybe Applications of Amperes Law is what might help you.

look at his whole playlist and it is pretty wide ranging.

Answer 10

Thanks for sharing this link.

Answer 11

@radar
my pleasure! it's an excellent free resource.

Answer 12

@IrishBoy123: Ohhhh it's just regular Algebra! I had no idea until now, that you can apply that concept to subscripts! Gee, Thanks!

As for that other video, Thank You for that too!

You've been a great help!

Answer 13

@Agent_A

brill!