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  • If the magnetic field in a plane electromagnetic wave is given by <img alt="\vec B=3\times10^{-8} sin (1.6\times10^3x + 48\times10^{10}t)\ \vec{j} \ T" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cvec%20B%3D3%5Ctimes10%5E%7B-8%7D%20sin%

If the magnetic field in a plane electromagnetic wave is given by \vec B=3\times10^{-8} sin (1.6\times10^3x + 48\times10^{10}t)\ \vec{j} \ T; then what will be the expression for the electric field?


Option: 1 \vec{E}=\left ( 9\sin \left ( 1.6\times 10^{3}x+48\times 10^{10}t \right )\widehat{k}\; V/m \right )
 
Option: 2 \vec{E}=\left ( 60\sin \left ( 1.6\times 10^{3}x+48\times 10^{10}t \right )\widehat{k}\; V/m \right )

Option: 3 \vec{E}=\left ( 3\times 10^{-8}\sin \left ( 1.6\times 10^{3}x+48\times 10^{10}t \right )\widehat{i}\; V/m \right )  

Option: 4 \vec{E}=\left ( 3\times 10^{-8}\sin \left ( 1.6\times 10^{3}x+48\times 10^{10}t \right )\widehat{j}\; V/m \right )
 

Answers (1)

best_answer

Nature of Electromagnetic Waves -

It is also seen from Maxwell’s equations that the magnitude of the electric and the magnetic fields in an electromagnetic wave are related as - B_{0}= \frac{E_o}{c}

given, \vec B=3\times10^{-8} sin (1.6\times10^3x + 48\times10^{10}t)T

\begin{aligned} \\ \left | \vec E \right |=BC=3\times10^{-8} sin (1.6\times10^3x + 48\times10^{10}t)\times (3\times10^8)\\ =9 sin (1.6\times10^3x + 48\times10^{10}t)T \end{aligned}

wave is propagating in -x direction, i.e., in - i direction.

the direction of the EMW wave is in the direction of \vec E\times \vec B.

Since B is in j direction and EMW is in -i direction. Therefore E is in (k) direction.

So Option (1) is correct.

Posted by

Ritika Jonwal

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