Skin depth of a cylinder coper

Calculate the skin depth
constants:c epsilon0 mu0


Parameters

frequency
f \(Hz\)
conductivity
`sigma` \(S/m\)
radius
a \(mm\)
length
L \(mm\)

Output

angular frequency `omega`

`omega=2 pi f`

resistivity `rho`

`rho=1/sigma`

`p^2` 

`p^2=j omega mu sigma`

k parameter ka

`ka=sqrt(omega mu sigma) a`

bessel function at the radius `J_0(pa)`

`abs(J_0(pa))`

skin depth `delta`

`delta=1/sqrt(pi f mu sigma)`

DC Resistance `R_{DC}`

`R_{DC}=l/(pi a^2 sigma)`

current area ratio 

`(pi a^2)/(2pi a delta)=a/(2 delta)`

AC resistance `R_{AC}`

`R_{AC}/R_{DC}=(pi a^2)/(2 pi a delta)=a/(2 delta)`

Inductance `L`

`(omega L)/(R_{DC})=a/(2 delta)`

critical frequency `f_{critical}`

`delta(f_c)=a`