A magnetic field vector in an electromagnetic wave is represented by \(\vec{B}={B}_{0}\sin \left(2\pi \nu t-\frac{2\pi x…
A magnetic field vector in an electromagnetic wave is represented by \(\vec{B}={B}_{0}\sin \left(2\pi \nu t-\frac{2\pi x}{\lambda }\right)\hat{j}\). Its associated electric field vector is ________
[JEE Main 2026, 4 Apr (Shift 2)]
\(\vec{E}=-\nu \lambda {B}_{0}\sin \left(2\pi \nu t-\frac{2\pi x}{\lambda }\right)\hat{k}\)
\(\vec{B}={B}_{0}\sin \left(2\pi \nu t-\frac{2\pi x}{\lambda }\right)\hat{j}\)
Since spatial term contains only \(x\) with negative sign \((\omega t-kx)\), wave propagates along \(+\hat{x}\).
\(\hat{E}\times \hat{B}=\hat{C}\)
\(\hat{B}=\hat{j},\hat{C}=\hat{j}\)
\(\hat{E}\times \hat{j}-\hat{i}\Rightarrow \hat{E}=-\hat{k}\)
\({E}_{0}=c{B}_{0}=\nu \lambda {B}_{0}\)
\(\vec{E}=-\nu \lambda {B}_{0}\sin \left(2\pi \nu t-\frac{2\pi x}{\lambda }\right)\hat{k}\)
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