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