Audrina Graham

2022-12-28

An electromagnetic wave has an electric field given by the expression (in Cartesian co-ordinates) : $\stackrel{\to }{E}\left(x,t\right)=6.0\mathrm{cos}\left(1.4×{10}^{7}x-3.43×{10}^{15}t\right)\stackrel{^}{z}$. What is the direction of the magnetic field at time t = 0 and position x = 0 ?
A. -x
B. +x
C. -y
D. +y

Collin Johns

Expert

$\because \stackrel{\to }{E}×\stackrel{\to }{B}||\stackrel{\to }{V}$
where $\stackrel{\to }{V}$ is a representation of the direction of propagation.
Given that wave is propagating along + x-axis and $\stackrel{\to }{E}$ along z-axis.
Therefore $\stackrel{\to }{E}×\stackrel{\to }{B}=+\stackrel{^}{i}$
$⇒\stackrel{^}{k}×\stackrel{\to }{B}=+\stackrel{^}{i}⇒\stackrel{\to }{B}$is along$-\stackrel{^}{j}$

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