The electric field of a plane electromagnetic wave in a medium is given by
\( E = 100 \sin (300z - 6 \times 10^{10}\,t)\,\mathrm{V\,m^{-1}} \)
The velocity of the electromagnetic wave in this medium will be
(Given: \( c \) - speed of light in vacuum)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 0.67\,c \)
For a wave \( E = E_0\sin(kz - \omega t) \), the wave speed is \( v = \omega/k \).
Comparing with the given field:
\( k = 300\,\mathrm{rad\,m^{-1}} \)
\( \omega = 6\times10^{10}\,\mathrm{rad\,s^{-1}} \)
\( \displaystyle v = \frac{\omega}{k} = \frac{6\times10^{10}}{300} = 2\times10^{8}\,\mathrm{m\,s^{-1}} \)
\( \displaystyle \frac{v}{c} = \frac{2\times10^{8}}{3\times10^{8}} = \frac{2}{3} \approx 0.67 \)
So \( v \approx 0.67\,c \). The wave is slower in the medium than in vacuum.