The electric field of an electromagnetic wave in free space is given by \overrightarrow E = 10\cos (10^7t + kx)\widehat 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 m. (2) the wave number k is 0.33 rad/m. (3) the wave amplitude is 10 V/m. (4) the wave is propagating along +x direction. Which one of the following pairs of statements is correct ?

Electromagnetic Waves question

2010 · Q82

Electromagnetic Waves question

2010 · Q82

View written solutionFree

Correct answer: D

As given, $E = 10\cos ({10^7}t + kx)\widehat j\,\,V/m$

here amplitude E₀ = 10 V/m and $\omega$ = 10⁷ rad/s

As c = $\nu \lambda = {{\omega \lambda } \over {2\pi }}$

$\Rightarrow$ $\lambda$ = ${{2\pi c} \over \omega }$ = ${{2\pi \times 3 \times {{10}^8}} \over {{{10}^7}}}$ = 188.4 m

Also, c = ${\omega \over k}$

$\Rightarrow$ k = ${\omega \over c} = {{{{10}^7}} \over {3 \times {{10}^8}}}$ = 0.033

The wave is propagating along y direction.

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Electromagnetic Waves question

2010 · Q82

Electromagnetic Waves question

2010 · Q82

View written solutionFree

Correct answer: D

As given, $E = 10\cos ({10^7}t + kx)\widehat j\,\,V/m$

here amplitude E₀ = 10 V/m and $\omega$ = 10⁷ rad/s

As c = $\nu \lambda = {{\omega \lambda } \over {2\pi }}$

$\Rightarrow$ $\lambda$ = ${{2\pi c} \over \omega }$ = ${{2\pi \times 3 \times {{10}^8}} \over {{{10}^7}}}$ = 188.4 m

Also, c = ${\omega \over k}$

$\Rightarrow$ k = ${\omega \over c} = {{{{10}^7}} \over {3 \times {{10}^8}}}$ = 0.033

The wave is propagating along y direction.