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The skin depth of copper is found to be 66 mm at 1 MHz at a certain temperature. At the same temperature and at 2 MHz, the skin depth would be approximately
  • a)
    47 μm
  • b)
    33 μm
  • c)
    92 μm
  • d)
    1.22 μm
Correct answer is option 'A'. Can you explain this answer?
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The skin depth of a material refers to the depth at which the electromagnetic field in the material decays to approximately 37% (1/e) of its original strength. It is a measure of how deeply the material can carry high-frequency currents.

Given:
Skin depth of copper at 1 MHz = 66 mm

To find:
Skin depth of copper at 2 MHz

Formula:
The skin depth (δ) can be calculated using the formula:

δ = √(2/πμσf)

where:
δ = skin depth
μ = permeability of the material
σ = conductivity of the material
f = frequency

Analysis:
In this case, the temperature is kept constant, so the permeability and conductivity of copper remain the same. We can assume that these values are constant for the given temperature.

We are given the skin depth at 1 MHz, so we can use this information to find the conductivity of copper.

Let's rearrange the formula to solve for σ:

σ = (2/πμδ²f)

Substituting the given values, we have:

σ = (2/πμ(66 mm)²(1 MHz))

Now, we can use the calculated conductivity to find the skin depth at 2 MHz.

δ = √(2/πμσf)

Substituting the values, we have:

δ = √(2/πμσ(2 MHz))

Solution:
To find the skin depth at 2 MHz, we need to calculate the conductivity of copper using the given information.

Once we have the conductivity, we can plug it into the formula to find the skin depth at 2 MHz.

The correct answer is option 'A' (47 μm)
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The skin depth of copper is found to be 66 mm at 1 MHz at a certain temperature. At the same temperature and at 2 MHz, the skin depth would be approximatelya)47 μmb)33 μmc)92 μmd)1.22 μmCorrect answer is option 'A'. Can you explain this answer?
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