Homework Help: Another E&M question

1. Apr 17, 2008

JohnDuck

1. The problem statement, all variables and given/known data
Calculate the power transported down the cables of Example 7.13 assuming the two conductors are held at potential difference V and carry current I.

The cable in example 7.13 is "a long coaxial cable" with inner radius a and outer radius b.

2. Relevant equations

Poynting's Theorem: $$\frac{dW}{dt} = -\frac{dU\sub{em}}{dt} - \int{\vec{S}\vec{da}}$$, where S is the Poynting vector and the integral is over a closed surface.

3. The attempt at a solution
Not confident my solution is correct. Seems somehow too easy. The first term of the LHS disappears because there is no time dependence. E is parallel to the z axis and has magnitude V/L at the surface of the outer wire, while B is circumferential and has magnitude $$\frac{\mu I}{2\pi s}$$. Thus S points radially inward and has magnitude $$\frac{VI}{2\pi sl}$$. The integral should be evaluated at the outer surface (s = b) over a cylindrical section of length L, yielding:

$$\int{\vec{S}\vec{da}} = S2\pi bL = VI$$

Like I said, I'm not confident my solution is correct (the book is very sparse on examples), and I'd like someone to confirm whether it is correct or incorrect.

2. Apr 17, 2008

Hootenanny

Staff Emeritus
You solution is indeed correct . You should have more confidence in yourself!