| The electric field of an electromagnetic wave in free space is given by |
| \[\overset{\to }{\mathop{\mathbf{E}}}\,=10\cos ({{10}^{7}}t+kx)\mathbf{\hat{j}}v/m,\] where t and x are in seconds and metres respectively. It can be inferred that [AIPMT (M) 2010] |
| (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? |
A) (3) and (4)
B) (1) and (2)
C) (2) and (3)
D) (1) and (3)
Correct Answer: D
Solution :
| The electric field of electromagnetic wave |
| \[\overset{\to }{\mathop{\mathbf{E}}}\,=10\cos ({{10}^{7}}t\pm kx)\,\mathbf{j}\] |
| Amplitude \[=10\text{ }V/m\] |
| \[\because \] \[c=\frac{\omega }{k}\] |
| \[\therefore \] \[3\times {{10}^{8}}=\frac{{{10}^{7}}}{k}\] |
| or \[k=\frac{1}{30}\] |
| or \[\frac{2\pi }{\lambda }=\frac{1}{30}\] |
| or \[\lambda =188.4\,\text{m}\] |
| So, (1) and (3) option are correct. |
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