JEE Mains · Physics · STD 12 - Electromagnetic waves
- JEE Mains 2019
- Medium
- MCQ
The electric field of a plane electromagnetic wave is given by \(\vec E = {E_0}\hat i\,\cos \,\left( {kz} \right)\,\cos \,\left( {\omega t} \right)\) The corresponding magnetic field \(\vec B\) is then given by
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(\vec B = \frac{{{E_0}}}{C}\hat j\,\sin \,\left( {kz} \right)\,\sin \,\left( {\omega t} \right)\)
Step-by-step Solution
Detailed explanation
\(\because \overrightarrow{\mathrm{E}} \times \overrightarrow{\mathrm{B}} \| \overrightarrow{\mathrm{v}}\)
Given that wave is propagating along positive \(z\) -axis and \(\overrightarrow{\mathrm{E}}\) along positive \(x\) -axis. Hence \(\overrightarrow{\mathrm{B}}\) along \(\mathrm{y}\) -axis.
From Maxwell equation
\(\overrightarrow{\mathrm{V}} \times \overrightarrow{\mathrm{E}}=-\frac{\partial \mathrm{B}}{\partial \mathrm{t}}\)
i.e. \(\frac{\partial E}{\partial Z}=-\frac{\partial B}{d t}\) and \(B_{0}=\frac{E_{0}}{C}\)
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