- #1

zenterix

- 555

- 76

- Homework Statement
- An inductor consists of two very thin conducting cylindrical shells, one of radius ##a## and one of radius ##b##, both of length ##h##.

This is shown in the two figures below.

Note in the rhs figure, we have the view of a cross-section and we have current flowing out of the page in the inner shell and into the page in the outer shell.

Assume that the current is uniformly distributed in both conductors and that ##b-a<<h## so that we can neglect edge effects.

- Relevant Equations
- What is the magnetic energy density for ##a<r<b##?

Calculate the inductance of this long inductor.

For ##a<r<b## we can calculate the magnetic field at some radius ##r## with Ampere's law

$$\oint_C\vec{B}\cdot d\vec{l}=\mu_0 I_{enc}=\mu_0 I$$

$$\implies B=\frac{\mu_0 I}{2\pi r}$$

$$\vec{B}=\frac{\mu_0 I}{2\pi r}\hat{\theta}$$

At this point my questions arise.

I don't see a current loop in this setup.

Therefore, I don't see an enclosed surface through which to compute a magnetic flux to be used in Faraday's law.

As far as I know, an inductor is pretty much any current loop because any current loop will produce a back emf due to a changing current in the loop.

I am not seeing why these coaxial cables form an inductor.