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  • An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y-direction has maximum magnitude of <img alt="\mathrm{60\; \mathrm{Vm}^{-1}}" src="/latex-image/?%

An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y-direction has maximum magnitude of \mathrm{60\; \mathrm{Vm}^{-1}}. Choose the correct equations for electric and magnetic fields if the EM wave is propagating in vacuum :

Option: 1

\begin{aligned} &\mathrm{E}_{y}=60 \sin \left[\frac{\pi}{4} \times 10^{3}\left(x-3 \times 10^{8} \mathrm{t}\right)\right] \hat{j} \mathrm{Vm}^{-1} \\ &\mathrm{~B}_{z}=2 \sin \left[\frac{\pi}{4} \times 10^{3}\left(x-3 \times 10^{8} \mathrm{t}\right)\right] \hat{k} \mathrm{~T} \end{aligned}


Option: 2

\begin{aligned} &\mathrm{E}_{y}=60 \sin \left[\frac{\pi}{4} \times 10^{3}\left(x-3 \times 10^{8} \mathrm{t}\right)\right] \hat{j} \mathrm{Vm}^{-1} \\ &\mathrm{~B}_{z}=2 \times 10^{-7} \sin \left[\frac{\pi}{4} \times 10^{3}\left(x-3 \times 10^{8} \mathrm{t}\right)\right] \hat{k} \mathrm{~T} \end{aligned}


Option: 3

\begin{aligned} &\mathrm{E}_{y}=2 \times 10^{-7} \sin \left[\frac{\pi}{4} \times 10^{3}\left(x-3 \times 10^{8} \mathrm{t}\right)\right] \hat{j} \mathrm{Vm}^{-1} \\ &\mathrm{~B}_{z}=60 \sin \left[\frac{\pi}{4} \times 10^{3}\left(x-3 \times 10^{8} \mathrm{t}\right)\right] \hat{k} \mathrm{~T} \end{aligned}


Option: 4

\begin{aligned} &\mathrm{E}_{y}=2 \times 10^{-7} \sin \left[\frac{\pi}{4} \times 10^{4}\left(x-4 \times 10^{8} \mathrm{t}\right)\right] \hat{j} \mathrm{Vm}^{-1} \\ &\mathrm{~B}_{z}=60 \sin \left[\frac{\pi}{4} \times 10^{4}\left(x-4 \times 10^{8} \mathrm{t}\right)\right] \hat{k} \mathrm{~T} \end{aligned}


Answers (1)

best_answer

\text{speed of wave in }\mathrm{vaccum =3 \times 10^{8} \mathrm{~m} / \mathrm{s}}
\begin{aligned} &E_{0}=C B_{0} \\ &B_{0}=\frac{60}{3 \times 10^{8}}=2 \times 10^{-7} \mathrm{~T} \end{aligned}
Hence option 2 is correct.

Posted by

Divya Prakash Singh

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