The image you uploaded contains a physics problem related to electrical conductivity. The question seems to involve calculating the skin depth when electromagnetic waves pass through a material, given its conductivity and wavelength.

Let me interpret the formula and calculations.

Key Information from the Question:

• Conductivity (σ) of copper: $5.8 \times 10^7 \, \Omega^{-1} \, \text{m}^{-1}$
• Wavelength: $10^{-4} \, \text{m}$ (this corresponds to the wavelength of the incident electromagnetic wave)

The question is asking about the skin depth of the material (copper) for this wavelength.

Formula for Skin Depth:

The skin depth $\delta$ is given by the formula:

$\delta = \sqrt{\frac{2}{\mu_0 \sigma \omega}}$

Where:

• $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7} \, \text{H/m}$),
• $\sigma$ is the electrical conductivity,
• $\omega$ is the angular frequency, which is related to the wavelength by:

$\omega = \frac{2 \pi c}{\lambda}$

Where $c$ is the speed of light in a vacuum ($3 \times 10^8 \, \text{m/s}$) and $\lambda$ is the wavelength.

Let's proceed by calculating the skin depth using the provided values.

I'll calculate it now. math

Given values

sigma = 5.8 * 107 # conductivity in S/m (ohm^-1 m^-1) wavelength = 10-4 # wavelength in meters mu_0 = 4 * math.pi * 10**-7 # permeability of free space in H/m (Henry per meter) c = 3 * 10**8 # speed of light in m/s

Angular frequency (omega)

omega = 2 * math.pi * c / wavelength

Skin depth (delta)

skin_depth = math.sqrt(2 / (mu_0 * sigma * omega)) skin_depthThe skin depth for copper, when subjected to electromagnetic waves with a wavelength of $10^{-4} \, \text{m}$, is approximately:

$\delta \approx 3.82 \times 10^{-8} \, \text{m} = 38.2 \, \text{nm}$

This indicates that the electromagnetic waves would penetrate up to a depth of about 38.2 nanometers into the copper material.

Would you like further details on this calculation or any clarifications? Here are some related questions you might find interesting:

1. How does conductivity affect the skin depth in different materials?
2. What is the relationship between wavelength and skin depth?
3. How does the permeability of free space impact the skin depth calculation?
4. Why does skin depth become smaller as conductivity increases?
5. What would happen to the skin depth if the wavelength were larger or smaller?

Tip: When working with electromagnetic waves and materials, the skin depth is crucial in understanding how materials absorb or reflect waves at different frequencies.