Q79 / 120 · NEET 2010 (Mains) · Physics

The electric field of an electromagnetic wave in free space is given by $\vec{E}=10 \cos \left(10^7 t+k x\right) \hat{j} V / m$, where $t$ and $x$ are in seconds and metres respectively. It can be inferred that (1) The wavelength $\lambda$ is $188.4 \mathrm{~m}$. (2) The wave number $k$ is $0.33 \mathrm{rad} / \mathrm{m}$. (3) The wave amplitude is $10 \mathrm{~V} / \mathrm{m}$. (4) The wave is propagating along.t $x$ direction Which one of the following pairs of statements is correct?

  • A
    (3) and (4)
  • B
    (1) and (2)
  • C
    (2) and (3)
  • Correct answer
    D
    (1) and (3)

Solution

The electric field of electromagnetic wave $$ \begin{aligned} & \overrightarrow{\mathrm{E}}=10 \cos \left(10^7 \mathrm{t} \pm \mathrm{kx}\right) \hat{\mathrm{j}} \\ & \text { Amplitude }=10 \mathrm{~V} / \mathrm{m} \\ & \because \quad \mathrm{c}=\frac{\omega}{\mathrm{k}} \\ & \therefore \quad 3 \times 10^8=\frac{10^7}{\mathrm{k}} \\ & \text { or } \quad k=\frac{1}{30} \\ & \text { or } \quad \frac{2 \pi}{\lambda}=\frac{1}{30} \\ & \text { or } \quad \lambda=188.4 \mathrm{~m} \\ & \end{aligned} $$ So, (1) and (3) option are correct.

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

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