First slide

Electromagnetic waves and its nature

Question

If the magnetic field of a plane electromagnetic wave is given by $B = 5 \times 10^{- 6} \sin [0.6 \times 10^{2} x + 0.5 \times 10^{10} t]$ then the speed of the wave is

Moderate

A

$0.83 \times 10^{7} m / s$
B

$0.83 \times 10^{8} m / s$
C

$5.24 \times 10^{8} m / s$
D

$5.24 \times 10^{9} m / s$

Solution

Given equation is $B = 5 \times 10^{- 6} \sin (0.6 \times 10^{2} x + 0.5 \times 10^{10} t) T$
Comparing the given equation with the equation of $B = B_{0} \sin (K x + ω t)$
Then $K = 0.6 \times 10^{2} m^{- 1}$ and $ω = 0.5 \times 10^{10} r a d / s$
Speed of the wave is $V = \frac{ω}{K} = \frac{0.5 \times 10^{10}}{0.6 \times 10^{2}} = \frac{5}{6} \times 10^{8}$
$\Rightarrow V = 0.83 \times 10^{8} m / s$

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