# Complex conductivity question

• Thierry12
In summary, the conversation discusses the equation for complex conductivity and its application to the penetration of light and radio waves in salt water. It is pointed out that the conductivity of salt water may not be a constant and may vary depending on factors such as frequency. This could explain why light waves, with a much higher frequency, are able to penetrate salt water while radio waves cannot. The importance of considering all relevant factors when using such equations is emphasized.

#### Thierry12

Can someone explain to me the equation on complex conductivity found here :
http://farside.ph.utexas.edu/teaching/jk1/lectures/node58.html" [Broken]

I am trying to understand why lightwaves penetrates salt water (conductor) but radiowaves can't.

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Good observation. The fact that light waves have a skin depth much deeper than what that formula seems to say they should is interesting, isn't it? But let's look at our assumptions. What numbers did you plug into the formula? The frequency of light is easy to find out. The magnetic permeability is a constant. But where did you get your value of conductivity of salt water? Is conductivity of salt water a constant?

I would think the answer to this question lies in the fact that salt water conducts by big, heavy ions (from the salt) moving around. And big, heavy ions don't like to move around as fast as TRILLIONS of Hertz (the frequency of light). This means that the resistance to extremely high frequencies would be extremely high. So the conductivity at a hundred trillion Hertz isn't the same number as the conductivity at DC (0 Hz), which is probably what you looked up.

The moral is: don't assume a number like conductivity of a substance is a constant! It may depend on other circumstances, like frequency.

## 1. What is complex conductivity?

Complex conductivity is a measure of the ability of a material to conduct electricity, taking into account both its resistance and its capacitance. It is represented by a complex number, with a real part representing the traditional conductivity and an imaginary part representing the capacitance.

## 2. How is complex conductivity different from traditional conductivity?

Traditional conductivity only takes into account the resistance of a material to conduct electricity, while complex conductivity also considers its capacitance. This allows for a more accurate representation of a material's electrical properties.

## 3. Why is complex conductivity important?

Complex conductivity is important because it provides a more complete understanding of how a material responds to an electrical current. This information is useful in fields such as materials science, engineering, and geophysics.

## 4. How is complex conductivity measured?

Complex conductivity is typically measured using a technique called electrical impedance spectroscopy, which involves applying a range of frequencies to a material and measuring its response. The resulting data can then be used to calculate the complex conductivity.

## 5. What are some applications of complex conductivity?

Complex conductivity has a wide range of applications, including analyzing the properties of materials, studying the electrical characteristics of geological formations, and designing electronic components. It is also used in medical imaging techniques such as magnetic resonance imaging (MRI).