The electric field vector associated with electromagnetic wave in free space is given by \( E = 40\cos\left(6 \times 10^{8}\,t - kx\right)\,\mathrm{V\,m^{-1}} \). The value of k in SI unit is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2
For a wave written as \( E_0\cos(\omega t - kx) \), the wave speed is \( \omega/k \). In free space an electromagnetic wave travels at the speed of light \( c \).
\( \omega = 6\times10^{8}\,\mathrm{rad\,s^{-1}} \)
\( c = 3\times10^{8}\,\mathrm{m\,s^{-1}} \)
\( \displaystyle k = \frac{\omega}{c} = \frac{6\times10^{8}}{3\times10^{8}} = 2\,\mathrm{rad\,m^{-1}} \)