Question

Example: Middle East College For silver the conductivity a-3M s/m, what frequency will the depth of penetration be 1 mm? Relative permeability of silver is 0.9999 Example: Find the depth of penetration of a plane wave in copper at a power frequency of 10 60 Hz and at a microwave frequency of 10 Hz. Given a -5.8x107 mho/m and Hr-6 (Hayt, 2006)

Answer 1

The penetration depth $\delta$ for a good conductor is given by

2 δ ωσμ Ν

where $\omega$ = angular frequency of the wave

$\sigma$= conductivity of the medium

$\mu$ = permeability of the medium

Part 1.For silver,

3M s/m 3 x 100 s/m 0.9999uo 0.9999 x 4m x 10 H/m

3 S1 mm 10 m

Frequency is given by

2 σμο 1 => f = 2 πσμα 3
[ since
w2T
]

Substituting the values of we get

0,u,

f 84.44 kH z

Therefore, for silver, at 84.44 kHz the penetration depth will be 1 mm.

Part 2. For copper

g5.8 x 10'mho/m ro6

Penetration depth at 60 Hz,

2 51 2T x 60 x 5.8 x 107 x 6 x 4X 10-73.48 mm

Penetration depth at ,

$\delta_2=\sqrt{\frac{2}{2\pi\times 10^{10}\times 5.8\times10^7\times 6\times 4\pi \times 10^{-7}}}=0.27 \,\mu m$