A solid conductor with relative permeability μ r = 200, conductiv
| A solid conductor with relative permeability μr = 200, conductivity σ = 5 × 106 mho/m having outer diameter 8 mm and length 2 mm. If the total current carried by the conductor is i(t) = 2 cos (π 104 t) A. Find the skin depth.
A. 2.25 mm
B. 0.225 mm
C. 0.16 mm
D. 1.60 mm
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Right Answer is: B
SOLUTION
Relative permeability (μr) = 200
Conductivity (σ) = 5 × 106 mho/m
Outer diameter of conductor = 8 mm
Length of conductor = 2 mm
Total current carried by conductor, i(t) = 2 cos (π × 104t) Amp
⇒ ω = π × 104 rad/sec
⇒ f = 0.5 × 104 Hz
\(\delta = \frac{1}{{\sqrt {\pi f\;\sigma \;{\mu _0}{\mu _r}} }}\)
\(\delta = \frac{1}{{\sqrt {\pi\; \times \;0.5\; \times \;{{10}^4}\; \times \;4\pi\; \times \;{{10}^{ - 7}}\; \times \;200\; \times \;5 \;\times\; {{10}^6}} }}\)
\(\Rightarrow \delta = \frac{1}{{\sqrt {2{\pi ^2}\; \times \;{{10}^6}} }} = 0.225\;mm\)