# Maxwell Equations in Conductors

1. May 5, 2014

### unscientific

1. The problem statement, all variables and given/known data

Part (a): Show wave equation for E can be reduced to that.
Part (b): Show impendance of material is:
Part (c): Find skin depth.

2. Relevant equations

3. The attempt at a solution

I've got parts (a) and (b) solved, part (c) I've worked it out, but I'm not sure how to use the information of senstivity of $1 \mu V m^{-1}$.

The characteristic timescale during transient state where charges flow in a conductor is $\tau = \frac{\epsilon_0 \epsilon_r}{\sigma}$.

For a low frequency regime, $\tau << \frac{1}{\omega}$.

Substituting, $\frac{\epsilon_r \epsilon_0}{\sigma} << \frac{1}{\omega}$ and finally $f << \frac{\sigma}{2\pi \epsilon_r \epsilon_0} = 0.01 Hz$.

Now to find skin depth, d:

$$d = \sqrt{\frac{2}{\mu_0 \mu_r \sigma \omega}}$$

Using $E = \frac{\sigma}{\epsilon_0 \epsilon_r}$,

$$d = \sqrt{\frac{2}{\mu_0 \mu_r \epsilon_0 \epsilon_r E \omega}} = 2.67 x 10^4 m$$

What's the point of giving the sensitivity of the receiver?

2. May 9, 2014

### unscientific

Maybe the sensitivity is simply there to say that after passing through a maximum depth $x_max$, the amplitude of the attenuated wave must be at least $1\mu Vm^{-1}$?

$$E = E_0 exp(-\frac{x}{d})$$

Let $E = 10^{-6}$:

This gives a value of $x_{max} = 4.92 \times 10^5 m$.

Last edited: May 9, 2014