The electric field of an electromagnetic wave is given as
\( \displaystyle E_z = 10\sin[2\pi\times10^{3}x + 10^{10}t]\,\frac{\mathrm{V}}{\mathrm{m}} \)
where \( x \) is in meter and \( t \) is in second. The wavelength of the wave is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1 mm
For a wave of the form \( \sin(kx + \omega t) \), the coefficient of \( x \) is the wave number \( k = 2\pi/\lambda \).
\( k = 2\pi\times10^{3}\,\mathrm{m^{-1}} \)
\( \displaystyle \lambda = \frac{2\pi}{k} = \frac{2\pi}{2\pi\times10^{3}}\,\mathrm{m} = 10^{-3}\,\mathrm{m} = 1\,\mathrm{mm} \)