geoana.em.fdem.skin_depth#

geoana.em.fdem.skin_depth(frequency, sigma, mu=1.25663706212e-06, epsilon=8.8541878128e-12, quasistatic=True)#

Compute skin depth for an electromagnetic wave in a homogeneous isotropic medium.

The skin depth is the propagation distance at which an EM planewave has decayed by a factor of \(1/e\). For a homogeneous medium with non-dispersive electrical conductivity \(\sigma\), magnetic permeability \(\mu\) and dielectric permittivity \(\varepsilon\), the skin depth for a wave at frequency \(f\) is given by:

\[\delta = \frac{1}{\omega} \Bigg (\frac{\mu \varepsilon}{2} \bigg [ \bigg ( 1 + \frac{\sigma^2}{\omega^2 \varepsilon^2} \bigg )^{1/2} - 1 \bigg ] \Bigg )^{1/2}\]

where \(\omega\) is the angular frequency:

\[\omega = 2 \pi f\]

For the quasistatic approximation, dielectric permittivity is ignore and the skin depth simplifies to:

\[\delta = \sqrt{\frac{2}{\omega \sigma \mu}}\]
Parameters
frequencyfloat, numpy.ndarray

frequency or frequencies (Hz)

sigmafloat

electrical conductivity (S/m)

mufloat (optional)

magnetic permeability (H/m). Default: \(\mu_0 = 4\pi \times 10^{-7}\) H/m

epsilonfloat (optional)

dielectric permittivity (F/m). Default: \(\epsilon_0 = 8.85 \times 10^{-12}\) F/m.

quasistaticbool (optional)

If True, the quasistatic approximation for the skin depth is computed.

Returns
float, (n_frequencies) numpy.ndarray

Skin depth for all frequencies provided