Question

The electric field of a certain plane electromagnetic wave is given by $E_{x}=0, E_{y}=0, E_{z}=2.0 \cos \left[\pi \times 10^{15}\left(t-\frac{x}{c}\right)\right] .$ The wave is propagating in the positive $x$-direction. Find the expressions for the components of the magnetic field of the wave.

• A. $B_{x}=0, B_{y}=6.7 \times 10^{-9} \cos \left[\pi \times 10^{16}(t-x / c)\right], B_{z}=0$
• B. $B_{x}=0, B_{y}=-6.7 \times 10^{-9} \cos \left[\pi \times 10^{15}(t-x / c)\right], B_{z}=0$
• C. $B_{x}=0, B_{y}=0, B_{z}=2.0 \cos \left[\pi \times 10^{15}(t-x / c)\right]$
• D. $B_{x}=0, B_{y}=0, B_{z}=-6.7 \times 10^{-9} \cos [\pi(t-x / c)]$

Answer 1

Answer: (B)

At plane, electromagnetic wave travelling with velocity $c=3 \times 10^{8} m / s$ along $x$-axis, then electric field vector $E$ is along $y$-axis while the magnetic field vector is along $z$-axis $B_{x}=0$
$B_{y}=-\frac{E_{z}}{C}=\frac{2.0 \cos \left[\pi \times 10^{15}(t-x / c)\right]}{3 \times 10^{8}} $
$B_{y}=-6.7 \times 10^{-9} \cos \left[\pi \times 10^{15}(t-x / c)\right] B_{z}=0$