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

Answer 1

Answer: (D)

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

Answer 2

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 ${{B}_{z}}=\frac{{{E}_{y}}}{c}\left( \frac{600}{3\times {{10}^{8}}} \right)\cos 2\pi \times {{10}^{11}}\left( t-\frac{x}{c} \right)$
$=22\times {{10}^{-8}}\cos 2\pi \times {{10}^{11}}\left( t-\frac{x}{c} \right)$
$=2.2\times {{10}^{-7}}\cos 2\pi \times {{10}^{11}}\left( t-\frac{x}{c} \right)$