A) For an electromagnetic wave propagating in \[+y\] direction the electric field is \[\vec{E}=\frac{1}{\sqrt{2}}{{E}_{yz}}\,(x,t)\,\hat{z}\] and the magnetic field is \[\overrightarrow{B}=\frac{1}{\sqrt{2}}{{B}_{z}}(x,t)\hat{y}\]
B) For an electromagnetic wave propagating in \[+y\] direction the electric field is \[\vec{E}=\frac{1}{\sqrt{2}}{{E}_{yz}}(x,t)\,\hat{z}\] and the magnetic field is \[\vec{B}=\frac{1}{\sqrt{2}}{{B}_{yz}}(x,t)\,\hat{y}\]
C) For an electromagnetic wave propagating in \[+x\] direction the electric field is \[\vec{E}=\frac{1}{\sqrt{2}}{{E}_{yz}}\,(y,\,\,z,\,\,t)\] \[\left( \hat{y}+\hat{z} \right)\] and the magnetic field is \[\vec{B}=\frac{1}{\sqrt{2}}{{B}_{yz}}\,(y,\,\,z,\,\,t)\,(\hat{y}+\hat{z})\]
D) For an electromagnetic wave propagating in \[+x\] direction the electric field is \[\vec{E}=\frac{1}{\sqrt{2}}{{E}_{yz}}\,(x,t)\,\left( \hat{y}-\hat{z} \right)\]and the magnetic field is \[\vec{B}=\frac{1}{\sqrt{2}}{{B}_{yz}}\,(x,t)\,\left( \hat{y}+\hat{z} \right)\]
Correct Answer: D
Solution :
[d] Wave in X-direction means E and B should be function of x and t. \[\overset{\scriptscriptstyle\frown}{y}-\overset{\scriptscriptstyle\frown}{z}\bot \overset{\scriptscriptstyle\frown}{y}+\overset{\scriptscriptstyle\frown}{z}\]
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