• # question_answer 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)

 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.