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# Engineering

An electromagnetic wave is represented by the electric field \hat{E}=E_{0}\hat{n}\sin\left[wt+(6y-8z) \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:

  • Option 1)

    \hat{s}=\frac{4\hat{j}-3\hat{k}}{5}

  • Option 2)

    \hat{s}=\frac{-4\hat{k}+3\hat{j}}{5}

  • Option 3)

    \hat{s}=\frac{3\hat{i}-4\hat{j}}{5}

  • Option 4)

    \hat{s}=\left ( \frac{-3\hat{j}+4\hat{k}}{5} \right )

 

Answers (1)
S solutionqc

 

Wave Equation -

E= E_{o} Sin w (t -\frac{x}{c})

E is in y-z plane

- wherein

E - Electric field at (x,t)

E0 - Electric field amplitude

\omega= Angular frequency

c= Speed of light in vacuum 

 

 

\vec{E}=E_{0}\hat{n}\sin \left[wt+(6y-8z) \right ]

\vec{E}=E_{0}\hat{n}\sin \left[wt-kx \right ]..................... General equation

direction of light

\hat{c}=\frac{-6\hat{j}+8\hat{k}}{\sqrt{6^{2}+8^{2}}}

\hat{c}=\frac{-6}{10}\hat{j}+\frac{8}{10}\hat{k}

\hat{c}=\frac{-3\hat{j}+4\hat{k}}{5}


Option 1)

\hat{s}=\frac{4\hat{j}-3\hat{k}}{5}

Option 2)

\hat{s}=\frac{-4\hat{k}+3\hat{j}}{5}

Option 3)

\hat{s}=\frac{3\hat{i}-4\hat{j}}{5}

Option 4)

\hat{s}=\left ( \frac{-3\hat{j}+4\hat{k}}{5} \right )

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