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  • The electric field in an electromagnetic wave is given by <img alt="\mathrm{E}=56.5 \sin \omega(\mathrm{t}-x / \mathrm{c}) \mathrm{NC}^{-1}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5C

The electric field in an electromagnetic wave is given by \mathrm{E}=56.5 \sin \omega(\mathrm{t}-x / \mathrm{c}) \mathrm{NC}^{-1}. Find the intensity of the wave if it is propagating along x-axis in the free space.
(Given \epsilon_{0}=8.85 \times 10^{-12} \mathrm{C}^{2} \mathrm{~N}^{-1} \mathrm{~m}^{-2} )
 

Option: 1

5.65 \mathrm{Wm}^{-2}


Option: 2

4.24 \mathrm{Wm}^{-2}


Option: 3

1.9 \times 10^{-7} \mathrm{Wm}^{-2}


Option: 4

56.5 \mathrm{Wm}^{-2}


Answers (1)

best_answer

\mathrm{E= 56.5\; \sin \left ( \omega \left ( t-\frac{x}{c} \right ) \right )}
\mathrm{Intensity= \frac{1}{2}\, \varepsilon _{0}\, E_{0}^{2}\, c}
                     \mathrm{= \frac{1}{2}\times \frac{1}{4\pi\times 9\times 10^{9}}\times \left ( 56.5 \right )^{2}\times \left ( 3\times 10^{8} \right )}

\mathrm{\left ( \because \; \frac{1}{4\pi \varepsilon _{0}}= 9\times 10^{9} \right )}
\mathrm{I= 4.24\: W/m^{2}}

The correct option is (2)

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mansi

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