A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive xdirection.

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A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction. At a particular point in space and time, $\vec{\text{E}} = 6.3\hat{\text{j}}\text{V/m}$. The corresponding magnetic field $\vec{\text{B}}$, at that point will be:

(1) 18.9x10-8 $\hat{\text{k}}$T

(2) 6.3x10-8 $\hat{\text{k}}$T

(3) 2.1x10-8 $\hat{\text{k}}$T

(4) 18.9x108 $\hat{\text{k}}$T

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Ans: (3) 2.1x10-8 $\hat{\text{k}}$T

Sol: $|\text{B}|={|\text{E}|\over \text{C}}={6.3\over3\times10^8}=2.1\times10^{-8}\text{T}$

and $\hat{\text{E}}\times\hat{\text{B}}=\hat{\text{C}}$

$\hat{\text{j}}\times\hat{\text{B}}=\hat{\text{i}}$

$\hat{\text{B}}=\hat{\text{k}}$

$\vec{\text{B}}=|\text{B}|\hat{\text{B}}=2.1\times10^{-8}\hat{\text{k}}\text{T}$