Calculating Self-Inductance in Coaxial Cables

[bon]

Homework Statement

A coaxial cable is made from concentric cylindrical conductors. The radius of the inner conductor is a and the outer comductor has inner radius b and outer radius d. Calculate the self inductance per unit length of the cable. You may assume that (b-a) >> a and (b-a) >> (d-b). Why is this assumption necessary.

Homework Equations

The Attempt at a Solution

Ok so i know that if we take the conducting plates to be think i can work out the inductance to be u0/2pi ln(b/a)

But what difference does it make that the outer one has an inner and outer radius? How do i work it out now?

Also why is the assumption necessary?

 

[bon]

Can Ampere's law always be applied without regard for what is outside the amperian loop?

So in this case, in the space between the inner cable and outer cable can i just draw an amperian loop and apply ampere's law? If so - why do i need to assume (b-a) >> a and (b-a) >> (d-b)?

Thanks

 

[bon]

anyone?

 

[bon]

should i post this in advanced phys?

 

[rwisz]

As a scientist, it is important to understand the underlying principles and assumptions behind any calculation. In this case, the assumption that (b-a) >> a and (b-a) >> (d-b) is necessary because it ensures that the inner conductor is significantly smaller than the outer conductor. This allows us to simplify the calculation and assume that the magnetic field lines are confined within the inner conductor, as the outer conductor essentially acts as a shield. If this assumption was not made, the calculation would become much more complex and may not accurately reflect the true self-inductance of the coaxial cable. Therefore, it is necessary to make this assumption in order to accurately calculate the self-inductance per unit length of the cable.