If the frequency of a plane electromagnetic wave increases four times, the depth of penetration, when is incident normally on a good conductor will Select one:a. decreases by a factor of 2b. increases by a factor of 2c. decreases by a factor of 4d. remains same
Question
If the frequency of a plane electromagnetic wave increases four times, the depth of penetration, when is incident normally on a good conductor will Select one:a. decreases by a factor of 2b. increases by a factor of 2c. decreases by a factor of 4d. remains same
Solution 1
When the frequency of a plane electromagnetic wave increases four times, the depth of penetration, when incident normally on a good conductor, will change. To determine how it changes, we can refer to the skin depth formula, which is given by:
δ = √(2/μσf)
Where: δ is the skin depth, μ is the permeability of the material, σ is the conductivity of the material, and f is the frequency of the electromagnetic wave.
In this case, since the frequency increases four times, we can substitute 4f into the formula:
δ' = √(2/μσ(4f))
Simplifying the equation, we get:
δ' = √(1/2μσf)
Comparing this with the original skin depth formula, we can see that the depth of penetration decreases by a factor of 2. Therefore, the correct answer is option a. The depth of penetration decreases by a factor of 2 when the frequency of a plane electromagnetic wave incident normally on a good conductor increases four times.
Solution 2
To answer this question, we need to understand the relationship between the frequency of an electromagnetic wave and the depth of penetration in a good conductor.
The depth of penetration refers to how far the electromagnetic wave can penetrate into the conductor before it is absorbed. It is determined by the skin depth, which is inversely proportional to the square root of the frequency.
Now, if the frequency of the wave increases four times, we can calculate the change in the depth of penetration. Let's assume the initial depth of penetration is D.
According to the relationship mentioned earlier, the new depth of penetration (D') can be calculated using the formula:
D' = D / √(4)
Simplifying this equation, we find that D' = D / 2.
Therefore, the new depth of penetration is half of the initial depth. This means that the depth of penetration decreases by a factor of 2 when the frequency of the plane electromagnetic wave increases four times.
So, the correct answer is option a. decreases by a factor of 2.
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