If electric field intensity of a uniform plane... | Electromagnetic Waves

JEE MAIN 2022

26-06-2022 S1

Question

If electric field intensity of a uniform plane electro magnetic wave is given as $$ E=-301.6 \sin (k z-\omega t) \hat{a}_x+452.4 \sin (k z-\omega t) \hat{a}_y \frac{V}{m} $$ Then, magnetic intensity H of this wave in $\mathrm{Am}^{-1}$ will be:' [Given: Speed of light in vacuum $\mathrm{c}=3 \times 10^8 \mathrm{~ms}^{-1}$, permeability of vacuum $\mu_0=4 \pi \times 10^{-7} \mathrm{NA}^{-2}$ ]

Select the correct option:

$+0.8 \sin (\mathrm{kz}-\omega \mathrm{t}) \hat{\mathrm{a}}_{\mathrm{y}}+0.8 \sin (\mathrm{kz}-\omega \mathrm{t}) \hat{\mathrm{a}}_{\mathrm{x}}$

$+1.0 \times 10^{-6} \sin (\mathrm{kz}-\omega \mathrm{t}) \hat{\mathrm{a}}_{\mathrm{y}}+1.5 \times 10^{-6}(\mathrm{kz}-\omega \mathrm{t}) \hat{\mathrm{a}}_{\mathrm{x}}$

$-0.8 \sin (\mathrm{kz}-\omega \mathrm{t}) \hat{\mathrm{a}}_{\mathrm{y}}-1.2 \sin (\mathrm{kz}-\omega \mathrm{t}) \hat{\mathrm{a}}_{\mathrm{x}}$

$-1.0 \times 10^{-6} \sin (k z-\omega t) \hat{a}_y-1.5 \times 10^{-6} \sin (k z-\omega t) \hat{a}_x$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$$ \begin{aligned} & \overline{\mathrm{E}}=301.6 \sin (\mathrm{k} z-\omega \mathrm{t})\left(-\hat{a}_{\mathrm{x}}\right)+452.4 \sin (\mathrm{k} z-\omega \mathrm{t}) \hat{a}_{\mathrm{y}} \\ & \overline{\mathrm{~B}}=\frac{301.6}{\mathrm{C}} \sin (\mathrm{k} z-\omega \mathrm{t})\left(-\hat{a}_{\mathrm{y}}\right) \\ & +\frac{452.4}{\mathrm{C}} \sin (\mathrm{k} z-\omega \mathrm{t})\left(-\hat{a}_{\mathrm{x}}\right) \\ & \overline{\mathrm{H}}=\frac{\overline{\mathrm{B}}}{\mu_0}=\frac{301.6}{\mu \mathrm{C}} \sin (\mathrm{k} z-\omega \mathrm{t})\left(-\hat{a}_{\mathrm{y}}\right) \\ & +\frac{452.4}{\mu \mathrm{C}} \sin (\mathrm{k} z-\omega \mathrm{t})\left(-\hat{a}_{\mathrm{x}}\right) \\ & \overline{\mathrm{H}}=-0.8 \sin (\mathrm{k} z-\omega \mathrm{t})\left(-\hat{a}_{\mathrm{y}}\right)-1.2 \sin (\mathrm{k} z-\omega \mathrm{t}) \hat{a}_{\mathrm{x}} \end{aligned} $$ For direction $$ \overline{\mathrm{E}} \times \overline{\mathrm{B}} \text {-is direction of } \overline{\mathrm{C}} $$ For first part $\hat{\mathrm{E}}=-\hat{\mathrm{i}}, \hat{\mathrm{B}}=$ ? $$ \hat{\mathrm{E}} \times \hat{\mathrm{B}}=\hat{\mathrm{k}} \Rightarrow \hat{\mathrm{~B}}=-\hat{\mathrm{j}} $$ Similarly for second $$ \begin{aligned} & \hat{\mathrm{E}} \times \hat{\mathrm{j}}, \hat{\mathrm{~B}}=? \\ & \hat{\mathrm{E}} \times \hat{\mathrm{B}}=\hat{\mathrm{k}} \Rightarrow \hat{\mathrm{~B}}=-\hat{\mathrm{i}} \end{aligned} $$

Question Tags

JEE Main

Physics

Hard

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