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A plane electromagnetic wave is propagating along the direction \frac{\hat{i}+\hat{j}}{\sqrt{2}}, with its polarization along the direction \hat{k}. The correct form the magnetic field of the wave would be (here B_{0} is an appropriate constant ) :
Option: 1 B_{0}\frac{\hat{i}-\hat{j}}{\sqrt{2}}\cos \left ( \omega t-k\frac{\hat{i+\hat{j}}}{\sqrt{2}} \right )      
Option: 2  B_{0}\frac{\hat{j}-\hat{i}}{\sqrt{2}}\cos \left ( \omega t+k\frac{\hat{i+\hat{j}}}{\sqrt{2}} \right )
Option: 3  B_{0}\frac{\hat{i}+\hat{j}}{\sqrt{2}}\cos \left ( \omega t-k\frac{\hat{i+\hat{j}}}{\sqrt{2}} \right )      
Option: 4 B_{0}\; \hat{k}\; \cos \left ( \omega t-k\frac{\hat{i+\hat{j}}}{\sqrt{2}} \right )
 

Answers (1)

best_answer

 

EM wave is in direction - \frac{\hat{i}+\hat{j}}{\sqrt{2}}

 

As we know that the axis of polarisation of the Em wave is same as Electric field direction that is -  \hat{k}

 

\vec{E}\times \vec{B} direction of propagation of EM wave = \frac{\hat{i}+\hat{j}}{\sqrt{2}}

 

                                                                        \Rightarrow \vec{k}\times \vec{B}=\frac{\hat{i}+\hat{j}}{\sqrt{2}} 

 

                                                          So  B is along                \Rightarrow \frac{\hat{i}-\hat{j}}{\sqrt{2}}

And the equation of the electromagnetic waves will be in terms of the  \cos (\omega t-\vec{K}\cdot \vec{r})

So by concluding the above result we can deduce that the option (1) is correct.

Posted by

avinash.dongre

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