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

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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