JEE Mains · Physics · STD 12 - Electromagnetic waves
- JEE Mains 2020
- Medium
- MCQ
The electric field of a plane electromagnetic wave is given by \(\overrightarrow{ E }= E _{0}(\hat{ x }+\hat{ y }) \sin ( kz -\omega t )\) Its magnetic field will be given by
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(\frac{ E _{0}}{ c }(-\hat{ x }+\hat{ y }) \sin ( kz -\omega t )\)
Step-by-step Solution
Detailed explanation
\(\overrightarrow{ E }= E _{0}(\hat{ x }+\hat{ y }) \sin ( kz -\omega t )\)
direction of propagation \(=+\hat{ k }\)
\(\hat{ E }=\frac{\hat{ i }+\hat{ j }}{\sqrt{2}}\)
\(\hat{ k }=\hat{ E } \times \hat{ B }\)
\(\hat{ k }=\left(\frac{\hat{ i }+\hat{ j }}{\sqrt{2}}\right) \times \hat{ B } \quad \Rightarrow \hat{ B }=\frac{-\hat{ i }+\hat{ j }}{\sqrt{2}}\)
\(\therefore \overrightarrow B =\frac{ E _{0}}{ C }(-\hat{ x }+\hat{ y }) \sin ( kz -\omega t )\)
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