First slide

Electromagnetic waves and its nature

Question

If the magnetic field of a plane electromagnetic wave is given by $B = 1 \times 10^{- 6} \sin [0.4 \times 10^{2} x + 0.3 \times 10^{10} t] T$ . Then the speed of the wave is

Easy

A

$0.75 \times 10^{7} m / s$
B

$0.75 \times 10^{8} m / s$
C

$1.33 \times 10^{9} m / s$
D

$1.33 \times 10^{7} m / s$

Solution

Given equation is $B = 1 \times 10^{- 6} \sin [0.4 \times 10^{2} x + 0.3 \times 10^{10} t] T$
Comparing the given equation with the equation of $B = B_{0} \sin [K x + ω t]$
Then $K = 0.4 \times 10^{2} m^{- 1} & ω = 0.3 \times 10^{10} r a d / s$
Speed of the wave is $V = \frac{ω}{K} = \frac{0.3}{0.4} \times \frac{10^{10}}{10^{2}} = \frac{3}{4} \times 10^{8}$
$\Rightarrow V = 0.75 \times 10^{8} m / s$

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