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NEET 2009
Exam
NEET
Year
2009
Subject
Physics
Chapter
Electromagnetic Waves

NEET 2009 · Physics · Electromagnetic Waves

The electric field part of an electromagnetic wave in a medium is...

The electric field part of an electromagnetic wave in a medium is represented by : Ex=0Ey=2.5NCcos⁡[(2π×106radm)t−(π×10−2rads)x]\begin{aligned}& \mathrm{E}_{\mathrm{x}}=0 \\ & \mathrm{E}_{\mathrm{y}}=2.5 \frac{\mathrm{N}}{\mathrm{C}} \cos \left[\left(2 \pi \times10^6 \frac{\mathrm{rad}}{\mathrm{m}}\right) \mathrm{t}-\left(\pi \times10^{-2} \frac{\mathrm{rad}}{\mathrm{s}}\right) \mathrm{x}\right] \end{aligned}E_z=0$. The wave is :

Options

  1. AMoving along - xx direction with frequency 106 Hz10^6 \mathrm{~Hz} and wavelength 200 m200 \mathrm{~m}
  2. BMoving along yy direction with frequency 2π×106 Hz2 \pi \times 10^6 \mathrm{~Hz} and wavelength 200 m200 \mathrm{~m}
  3. CMoving along xx direction with frequency 10610^6 Hz\mathrm{Hz} and wavelength 100 m100 \mathrm{~m}
  4. DMoving along xx direction with frequency 10610^6 Hz\mathrm{Hz} and wavelength 200 m200 \mathrm{~m}

Correct answer

D. Moving along xx direction with frequency 10610^6 Hz\mathrm{Hz} and wavelength 200 m200 \mathrm{~m}

Step-by-step solution

As the coefficient of xx is negative, it is moving along +ve xx-axis and equating the equation \begin{aligned} \mathrm{E}_{\mathrm{y}} & =2.5 \cos \left[\left(2 \pi \times 10^6\right) \mathrm{t}-\left(\pi \times 10^{-2}\right) \mathrm{x}\right] \\ \text{ with } \mathrm{y} & =\mathrm{A} \cos (\omega \mathrm{t}-\mathrm{kx}) \\ \omega & =2 \pi \times 106 \\ \Rightarrow \mathrm{f} & =\frac{\omega}{2 \pi}=10^6 \mathrm{~Hz} \\ \mathrm{k} & =\pi \times 10^{-2} \\ \Rightarrow \quad \lambda & =\frac{2 \pi}{\mathrm{k}} \\ & =\frac{2 \pi}{\pi \times 10^{-2}}=200 \mathrm{~m} \end{aligned}
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