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For a continuous sinusoidal electromagnetic wave, which relation holds true for peak intensity (I₀) and average intensity (Iₐᵥₑ)?

a) I₀ = Iₐᵥₑ
b) I₀ = 2Iₐᵥₑ
c) I₀ = √2Iₐᵥₑ
d) I₀ = 4Iₐᵥₑ

User Defoo
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Final answer:

The peak intensity (I₀) of a continuous sinusoidal electromagnetic wave is twice the average intensity (Iₐᵥₑ), using the relationship between peak and rms values of electric and magnetic fields (E₀ and B₀). Therefore, the correct option is b).

Step-by-step explanation:

In the context of electromagnetic waves, the intensity of a wave is related to the square of its amplitude. For a continuous sinusoidal electromagnetic wave, the energy carried and the intensity (I) are proportional to the square of the electric field (E²) and the magnetic field (B²). By utilizing the relationship between the peak values and root mean square (rms) values of the electric and magnetic fields (E₀ = √2Eₙₘₛ and B₀ = √2Bₙₘₛ), you can deduce that the peak intensity (I₀) is twice the average intensity (Iₐᵥₑ).

This is because rms values are a type of average that indicates the square root of the mean of the squares of the values, which for a sinusoidal wave, equates to Eₙₘₛ = E₀/√2 and Bₙₘₛ = B₀/√2. Hence, when these rms values are squared as in the calculation of intensity, the factor of 1/2 from the rms calculation is effectively removed, yielding an intensity that is related to the square of the peak values. Thus, for a sinusoidal wave, this implies that I₀ = 2Iₐᵥₑ, showcasing that the peak intensity is indeed twice the average intensity.

User Wazeed
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