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  4. The magnetic field in a plane electromagnetic wave is given by =2 × 10-7 sin (0.5 × 103 x+1.5 × 1011 t). This electromagnetic wave is

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Q. The magnetic field in a plane electromagnetic wave is given by $=2 \times 10^{-7} \sin \left(0.5 \times 10^{3} x+1.5 \times 10^{11} t\right)$. This electromagnetic wave is

Electromagnetic Waves

Solution:

$B=2 \times 10^{-7} \sin \left(0.5 \times 10^{-3} x+1.5 \times 10^{11} t\right)$
$f=\frac{c}{\lambda}, $
$k=0.5 \times 10^{-3}$
$\omega=1.5 \times 10^{11}$
${V=\frac{\omega}{k}=} \frac{1.5 \times 10^{11}}{0.5 \times 10^{-3}}$
$=3 \times 10^{14}$
$\frac{\omega}{k}=f \lambda$
$k=\frac{2 \pi}{\lambda}$
$\therefore \lambda=\frac{2 \pi}{k}=\frac{2 \times 22}{7 \times 0.5 \times 10^{-3}}$
$=\underset{\text{Radio waves}}{1.25 \times 10^{4} m}$