Question
Download Solution PDFThe electric field in an electromagnetic wave is given by E = 56.5 sin ω(t − x/c) NC−1. Find the intensity of the wave if it is propagating along x-axis in the free space.
(Given ϵ0 = 8.85 × 10−12 C2N−1m−2)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
The intensity of the electromagnetic wave is written as;
I = \(\frac{1}{2} \epsilon_o E^2_oc\) -----(1)
Here we have "I" as intensity, ϵ0 as permittivity of the free space, E is the electric field and c is the velocity of light.
CALCULATION:
Given:
E = 56.5 sin ω(t − x/c) NC-1
The velocity of light, c = 3 × 108 m/s
and permittivity of the free space,ϵ0 = 8.85 \(×\) 10-12
Now for the calculation of intensity, we are using equation (1) we have;
I = \(\frac{1}{2} \epsilon_o E^2_oc\)
⇒ I = \(\frac{1}{2}× 8.85 × 10 ^{-12} × 56.5^2× 3 × 10 ^8\)
⇒ I = \( 4.425 × 10 ^{-4} × 3192.25× 3 \)
⇒ I = 42377.11875 \(×\) 10-4
⇒ I = 4.24 Wm-2
Hence, option 2) is the correct answer.
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