A monochromatic beam of light has a frequency v= \frac{3}{2\pi }\times 10^{12}Hz and is propagating along the direction \frac{\hat{i}+\hat{j}}{\sqrt{2}}It is polarized along the \hat{k} direction. Then acceptable form for the magnetic field is :

  • Option 1)

    \frac{E_{o}}{C} \frac{(\hat{i} - \hat{j})}{\sqrt{2}} \cos \left [ 10^{4} \frac{(\hat{i} + \hat{j})}{\sqrt{2}}.\overrightarrow{r}-(3\times10 ^{12})t\right ]

     

     

     

  • Option 2)

    \frac{E_{o}}{C} \frac{(\hat{i} - \hat{j})}{\sqrt{2}} \cos \left [ 10^{4} \frac{(\hat{i} -\hat{j})}{\sqrt{2}}.\overrightarrow{r}-(3\times10 ^{12})t\right ]

  • Option 3)

    \frac{E_{o}}{C} \hat{k} \cos \left [ 10^{4} \frac{(\hat{i} +\hat{j})}{\sqrt{2}}.\overrightarrow{r}+(3\times10 ^{12})t\right ]

  • Option 4)

    \frac{E_{o}}{C} \frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}} \cos \left [ 10^{4} \frac{(\hat{i} +\hat{j})}{\sqrt{2}}.\overrightarrow{r}+(3\times10 ^{12})t\right ]

 

Answers (2)
N neha
V Vakul

As we learned

 

Poynting Vector -

\underset{S}{\rightarrow} = \frac{\underset{E}{\rightarrow} \times \underset{B}{\rightarrow}}{\mu_{o}}

- wherein

It is total energy flowing perpendicularly per second per unit area into the surface in free space.

 

 \vec{E}\times\vec{B} should give a direction of wave propagation

\Rightarrow \vec{E}\times\vec{B} \parallel \frac{\hat{i}+\hat{j}}{\sqrt{2}}

option (1) \hat{k}\times \left ( \frac{\hat{i}+\hat{j}}{\sqrt{2}} \right )=\frac{\hat{j}-\hat{i}}{\sqrt{2}}\parallel \frac{\hat{i}-\hat{j}}{\sqrt{2}}

option (2) and (4) does not satisfy this wave propagation vector should be along \frac{\hat{i}+\hat{j}}{\sqrt{2}}

 

 


Option 1)

\frac{E_{o}}{C} \frac{(\hat{i} - \hat{j})}{\sqrt{2}} \cos \left [ 10^{4} \frac{(\hat{i} + \hat{j})}{\sqrt{2}}.\overrightarrow{r}-(3\times10 ^{12})t\right ]

 

 

 

Option 2)

\frac{E_{o}}{C} \frac{(\hat{i} - \hat{j})}{\sqrt{2}} \cos \left [ 10^{4} \frac{(\hat{i} -\hat{j})}{\sqrt{2}}.\overrightarrow{r}-(3\times10 ^{12})t\right ]

Option 3)

\frac{E_{o}}{C} \hat{k} \cos \left [ 10^{4} \frac{(\hat{i} +\hat{j})}{\sqrt{2}}.\overrightarrow{r}+(3\times10 ^{12})t\right ]

Option 4)

\frac{E_{o}}{C} \frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}} \cos \left [ 10^{4} \frac{(\hat{i} +\hat{j})}{\sqrt{2}}.\overrightarrow{r}+(3\times10 ^{12})t\right ]

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