Answer :
Final answer:
The skin depth, d, at a frequency of 1.6 MHz in aluminum is approximately 6.58 μm and the phase velocity, U, is about 6.2 m/s.
Explanation:
The concept applied here is that of Electromagnetic theory in Physics. To find the skin depth, the formula d = sqrt(2/(ωμσ)) is employed
where ω = 2π*f (frequency), μ is the permeabilty and σ is the conductivity. With your values, the frequency, f, is 1.6 MHz, so ω = 2*π*1.6*10^6, and μ = 1, and σ = 38.2 mho/m.
For wave velocity, U (also termed as the phase velocity), the formula used is U = ω/k where k (wave number) is equal to ω/√(μσ). After calculating ω and k, the value of U can be found by simply dividing ω by k.
Example Calculation
Let's plug in and calculate:
- First, ω = 2π*frequency = 2π*1.6*10^6 = 10.05*10^6 rad/sec
- Second, by placing the values in the formula of d, we get d = sqrt( 2 / (10.05*10^6 * 1 * 38.2) ) = 6.58*10^-6 m = 6.58 μm.
- For wave velocity, first compute k = ω/√(μσ) = (10.05*10^6) / √(1 * 38.2) = 1.62*10^6 m^-1
- Finally, U = ω/k = (10.05*10^6) / (1.62*10^6) = 6.2 m/s
In conclusion, the skin depth, d, at a frequency of 1.6 MHz in aluminum is approximately 6.58 μm and the phase velocity, U, is about 6.2 m/s.
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