JEE Mains · Physics · STD 12 - Electromagnetic waves
- JEE Mains 2019
- Medium
- MCQ
An electromagnetic wave is represented by the electric field \(\vec E = {E_0}\hat n\,\sin \,\left[ {\omega t + \left( {6y - 8z} \right)} \right]\). Taking unit vectors in \(x, y\) and \(z\) directions to be \(\hat i,\hat j,\hat k\) ,the direction of propogation \(\hat s\), is
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(\hat S = \left( {\frac{{ - 3\hat j + 4\hat k}}{5}} \right)\)
Step-by-step Solution
Detailed explanation
\(\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \hat{\mathrm{n}} \sin \left(\omega \mathrm{t}+(6 \mathrm{y}-8 \mathrm{z})=\mathrm{E}_{0} \hat{\mathrm{n}} \sin (\omega \mathrm{t}+\overrightarrow{\mathrm{k}} \cdot \overrightarrow{\mathrm{r}})\right.\)
where \(\vec{r}=x \hat{i}+y \hat{j}+z \hat{k}\) and \(\vec{k} \cdot \vec{r}=6 y-8 z\)
\(\Rightarrow \overrightarrow{\mathrm{k}}=6 \hat{\mathrm{j}}-8 \hat{\mathrm{k}}\)
\(\text { direction of propagation } \hat{\mathrm{s}} =-\hat{\mathrm{k}}\)
\( =\left(\frac{-3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}}{5}\right) \)
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