Question

A plane electromagnetic wave travelling along the $ X- $ direction has a wavelength of $ 3 \,mm $ . The variation in the electric field occurs in the $ Y- $ direction with an amplitude $ 66\,V{{m}^{-1}} $ . The equations for the electric and magnetic fields as a function of $ x $ and $t$ are respectively.

• A. $ {{E}_{y}}=33\,\cos \pi \times {{10}^{11}}\left( t-\frac{x}{c} \right), $ $ {{B}_{z}}=1.1\times {{10}^{-7}}\cos \pi \times {{10}^{11}}\left( t-\frac{x}{c} \right) $
• B. $ {{E}_{y}}=11\,\cos 2\pi \times {{10}^{11}}\left( t-\frac{x}{c} \right), $ $ {{B}_{y}}=11\times {{10}^{-7}}\cos 2\pi \times {{10}^{11}}\left( t-\frac{x}{c} \right) $
• C. $ {{E}_{x}}=33\,\cos \pi \times {{10}^{11}}\left( t-\frac{x}{c} \right), $ $ {{B}_{x}}=11\times {{10}^{-7}}\cos \pi \times {{10}^{11}}\left( t-\frac{x}{c} \right) $
• D. $ {{E}_{y}}=66\,\cos 2\pi \times {{10}^{11}}\left( t-\frac{x}{c} \right), $ $ {{B}_{z}}=2.2\times {{10}^{-7}}\cos 2\pi \times {{10}^{11}}\left( t-\frac{x}{c} \right) $
• E. $ {{E}_{y}}=66\,\cos \pi \times {{10}^{11}}\left( t-\frac{x}{c} \right), $ $ {{B}_{y}}=2.2\times {{10}^{-7}}\,\cos \pi \times {{10}^{11}}\left( t-\frac{x}{c} \right) $

Answer 1

Answer: (D)

The equation of electric field occurring in Y-direction $ {{E}_{y}}=66\,\cos 2\pi \times {{10}^{11}}\left( t-\frac{x}{c} \right) $
Therefore, for the magnetic field in Z-direction $ {{B}_{z}}=\frac{{{E}_{y}}}{c}\left( \frac{600}{3\times {{10}^{8}}} \right)\cos 2\pi \times {{10}^{11}}\left( t-\frac{x}{c} \right) $
$ =22\times {{10}^{-8}}\cos 2\pi \times {{10}^{11}}\left( t-\frac{x}{c} \right) $
$ =2.2\times {{10}^{-7}}\cos 2\pi \times {{10}^{11}}\left( t-\frac{x}{c} \right) $