A) \[\overset{\to }{\mathop{B}}\,(x.t)=(9\times {{10}^{-8}}T)\hat{i}\] \[\sin \left[ 2\pi (1.5\times {{10}^{-8}}x-2\times {{10}^{14}}t) \right]\]
B) \[\overset{\to }{\mathop{B}}\,(x,t)=(3\times {{10}^{-8}}T)\hat{j}\] \[\sin \left[ 1.5\times {{10}^{-6}}x-2\times {{10}^{14}}t) \right]\]
C) \[\overset{\to }{\mathop{B}}\,(x,t)=(3\times {{10}^{-8}}T)\hat{j}\] \[\sin \left[ 2\pi (1.5\times {{10}^{-8}}x-2\times {{10}^{14}}t) \right]\]
D) \[\overset{\to }{\mathop{B}}\,(x,t)=(9\times {{10}^{-8}}T)\hat{k}\] \[\sin \left[ 2\pi (1.5\times {{10}^{-6}}x-2\times {{10}^{14}}t) \right]\]
E) None of the above
Correct Answer: E
Solution :
Enwove \[f=2\times {{10}^{14}}Hz\] \[{{E}_{0}}=27V/m\] We know \[\to \frac{E}{B}=C\] so \[B=\frac{27}{3\times {{10}^{8}}}=9\times {{10}^{-8}}T\] now for \[\lambda =\frac{3\times {{10}^{8}}}{2\times {{10}^{17}}}=1.5\times {{10}^{-6}}m\] so \[B=9\times {{10}^{-8}}\sin \left( 2\pi \left[ \left( \frac{1}{1.5\times {{10}^{-6}}} \right)x-2\times {{10}^{14}}t \right] \right)\hat{k}\]
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