An electromagnetic wave with frequency omega | vedclass

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Question

(C) In an electromagnetic wave, the electric field $\vec{E}$, magnetic field $\vec{B}$, and the direction of propagation $\vec{k}$ are mutually perpen

Vedclass · Accepted Answer

$\vec{E} = E_0 \cos \left( \omega t - \frac{2\pi}{\lambda} y \right) \hat{z}$

Vedclass · Answer

(C) In an electromagnetic wave, the electric field $\vec{E}$, magnetic field $\vec{B}$, and the direction of propagation $\vec{k}$ are mutually perpendicular.Given that the wave propagates in the $+y$ direction, the wave vector is along the $y$-axis.The magnetic field $\vec{B}$ is along the $+x$ axis.Since the direction of propagation is given by the cross product of the electric and magnetic fields $(\vec{E} 	imes \vec{B} \propto \vec{v})$, we have $\hat{E} 	imes \hat{x} = \hat{y}$.This implies that the electric field must be along the $z$-axis (since $\hat{z} 	imes \hat{x} = \hat{y}$).For a wave traveling in the $+y$ direction, the phase term is $(\omega t - ky)$, where $k = \frac{2\pi}{\lambda}$.Therefore, the electric field vector is $\vec{E} = E_0 \cos \left( \omega t - \frac{2\pi}{\lambda} y ight) \hat{z}$.

An electromagnetic wave with frequency $\omega$ and wavelength $\lambda$ travels in the $+y$ direction. Its magnetic field is along the $+x$ axis. The vector equation for the associated electric field (of amplitude $E_0$) is:

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