# What is Skin depth formula in electromagnetic waves

Skin effect is a phenomenon that occurs in conductors carrying alternating current (AC) at high frequencies. It describes the tendency of AC current to concentrate near the outer surface, or "skin," of the conductor, while the inner regions carry less current. This effect is caused by the behavior of electromagnetic waves in conductive materials and has important implications in electrical engineering and transmission line design.

This effect is described by the skin depth, which is a measure of how deeply EM fields such as radio waves or alternating current, penetrate into a conductor like copper. It is an important parameter in electrical engineering and is dependent on the frequency of the signal passing through the conductor. Following skin depth formula is used to calculate skin depth in a conductor like copper. It is measured in units of meters or µmeters or milli-meters.

A skin depth calculator is a tool or software application that helps engineers and scientists quickly determine the skin depth of a conductor for a given set of parameters, such as the material's resistivity, permeability and the frequency of the AC signal or electromagnetic wave.

## Skin Depth Calculator

➤Following calculator is used to calculate skin depth.

➤Enter values in INPUT boxes and Press CALCULATE button to check OUTPUT.

EXAMPLE of skin depth calculator :

INPUTS: Frequency (MHz) = 2400 , Conductivity of material = 1.678 x 10^{-8} Ohm-meter,
Relative permittivity of material = 0.999994

OUTPUT: Skin depth (Meters) = 0.00000133079

## How to calculate skin depth of copper

To understand the concept let us take example of copper wire and analyze effect of frequency.
The resistivity of copper at room temperature is 1.678 x 10^{-8} Ohm*m and
its relative permeability is 0.999994

• Case-1 : Take AC frequency of 60 Hz (Enter 60E-6 in calculator), calculate skin depth using above calculator , which is about 0.00841669 meters (i.e. 8.41 mm)

• Case-2 : Take EM frequency of 3500 MHz, calculate skin depth using above calculator, which is about 0.000001102 meters (i.e. 1.102 µm)

➨From skin depth calculations at different frequencies we can conclude that skin effect is almost negligible at AC frequencies of
60 Hz in our home. Moreover at radio frequencies (RF) with 3.5 GHz (i.e. 3500 MHz) also current flows only through extremely thin portion
near the surface which is few µmeters.

**Conclusion** : Overall, skin depth calculator and skin depth formula provide a convenient and efficient way to incorporate the effects of the skin effect into the
design and analysis of electrical and electromagnetic systems.

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