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  • The electric field of a plane electromagnetic wave is given by <img alt="\overrightarrow{E}=E_{0}\left ( \widehat{x}+\widehat{y} \right )\sin (kz- \omega t)" src="http://entrancecorner.codecogs.com/gif.latex?%5Coverrightarrow%7BE%7D%3DE_%7B0%7D%5Cleft%

The electric field of a plane electromagnetic wave is given by \overrightarrow{E}=E_{0}\left ( \widehat{x}+\widehat{y} \right )\sin (kz- \omega t) Its magnetic field will be given by:
Option: 1 \frac{E_{0}}{c}(-\widehat{x}+\widehat{y})\sin (kz-\omega t)
Option: 2 \frac{E_{0}}{c}(\widehat{x}+\widehat{y})\sin (kz-\omega t)
Option: 3 \frac{E_{0}}{c}(\widehat{x}-\widehat{y})\sin (kz-\omega t)
Option: 4 \frac{E_{0}}{c}(\widehat{x}-\widehat{y})\cos (kz-\omega t)

Answers (1)

best_answer

\begin{aligned} &\overrightarrow{\mathbf{E}} \times \overrightarrow{\mathbf{B}} \text { is along } \overrightarrow{\mathbf{C}}\\ &\hat{\mathbf{E}} \times \hat{\mathbf{B}}=\hat{\mathbf{C}}\\ \end{aligned}

Since the electric field is given in the question is  - 

\overrightarrow{E}=E_{0}\left ( \widehat{x}+\widehat{y} \right )\sin (kz- \omega t)

So by the  cross product we can say that - 
\Rightarrow \overrightarrow{\mathbf{B}}=\frac{\mathbf{E}_{0}}{\mathbf{C}}(-\hat{\mathbf{x}}+\hat{\mathbf{y}}) \sin (\mathbf{k z}-\omega \mathbf{t})

Posted by

Deependra Verma

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