A plane electromagnetic wave travels through a medium and the magnetic field associated with it is given by
$$B = 5 \times 10^{-8} \sin (3 \times 10^{10} t - 150 x) T$$
where x is in metres and t is in seconds.
The velocity of the wave is :
(A) $$2.0 \times 10^{8} ms^{-1}$$
(B) $$4.5 \times 10^{7} ms^{-1}$$
(C) $$3.5 \times 10^{7} ms^{-1}$$
(D) $$2.5 \times 10^{8} ms^{-1}$$
EASY
Correct AnswerA
EXPLANATION
Compare with the Standard Wave Equation:The general equation for a plane electromagnetic wave travelling along the x-axis is given by:$$B = B_0 \sin(\omega t - kx)$$Comparing this with the given equation:$$B = 5 \times 10^{-8} \sin(3 \times 10^{10} t - 150 x)$$Extract the Wave Parameters:Angular frequency ($\omega$) = $3 \times 10^{10} \text{ rad s}^{-1}$Propagation constant / Wave number ($k$) = $150 \text{ rad m}^{-1}$Calculate the Velocity of the Wave:The phase velocity ($v$) of an electromagnetic wave in a medium is related to $\omega$ and $k$ by the formula:$$v = \frac{\omega}{k}$$Substitute the values:$$v = \frac{3 \times 10^{10}}{150} = \frac{3 \times 10^{10}}{1.5 \times 10^2} = 2.0 \times 10^8 \text{ ms}^{-1}$$
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