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A plane electromagnetic wave having a frequency $n = 23.9\, GHz$ propagates along the positive $z-$ direction in free space. The peak value of the electric field is $60\, V/m$. Which among the following is the acceptable magnetic field component in the electromagnetic wave?
$\vec B = 2 \times {10^{ - 7}}\,\sin \,\left( {1.5 \times {{10}^2}x + 0.5 \times {{10}^{11}}t} \right)\hat j$
$\vec B = 60\,\sin \,\left( {0.5 \times {{10}^3}x + 1.5 \times {{10}^{11}}t} \right)\hat k$
$\vec B = 2 \times {10^{ - 7}}\,\sin \,\left( {0.5 \times {{10}^2}z - 1.5 \times {{10}^{11}}t} \right)\hat i$
$\vec B = 2 \times {10^{7}}\,\sin \,\left( {0.5 \times {{10}^3}z + 1.5 \times {{10}^{11}}t} \right)\hat i$
Solution
Magnetic field when electromagnetic wave propagates in $+z$ direction.
$\mathrm{B}=\mathrm{B}_{0} \sin (\mathrm{kz}-\omega \mathrm{t})$
where
$\mathrm{B}_{0}-\frac{60}{3 \times 10^{8}}=2 \times 10^{-7}$
$\mathrm{k}=\frac{2 \pi}{\lambda}=0.5 \times 10^{3}$
$\omega=2 \pi \mathrm{f}=1.5 \times 10^{11}$
