Q154 / 160 · TS EAMCET 2018 (04 May Shift 2) · Physics

If the magnetic field of a plane electromagnetic wave is given by $5 \times 10^{-6} \sin \left(0.6 \times 10^2 x+0.5 \times 10^{10} t\right)$, then the speed of the wave is

  • A
    $0.83 \times 10^7 \mathrm{~m} / \mathrm{s}$
  • Correct answer
    B
    $0.83 \times 10^8 \mathrm{~m} / \mathrm{s}$
  • C
    $5.24 \times 10^8 \mathrm{~m} / \mathrm{s}$
  • D
    $5.24 \times 10^9 \mathrm{~m} / \mathrm{s}$

Solution

$\begin{aligned} \text { Given, } k & =\frac{2 \pi}{\lambda}=0.6 \times 10^2 \mathrm{~m}^{-1} \\ \omega & =\frac{2 \pi}{T}=0.5 \times 10^{10} \mathrm{~s}^{-1} \\ \Rightarrow \text { Velocity, } \quad v & =\omega / k=\frac{2 \pi}{T} \times \frac{\lambda}{2 \pi}=\frac{0.5 \times 10^{10}}{0.6 \times 10^2} \\ v & =0.83 \times 10^8 \mathrm{~m} / \mathrm{s} \end{aligned}$

Hence, the correct answer is option: 'B'.

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