A plane electromagnetic wave of frequency 25 GHz is propagating in vacuum along the z-direction. At a particular point in space and time, the magnetic field is given by a value \( 5\times10^{-8}\,\mathrm{T} \) along Y-direction. The corresponding electric field is
(speed of light \( c = 3\times10^{8}\,\mathrm{m/s} \))
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 15 V/m, along +X axis
In an electromagnetic wave the field magnitudes are related by \( E = cB \), and the wave travels along \( \vec{E}\times\vec{B} \). The frequency is not needed.
\( \displaystyle E = cB = 3\times10^{8}\,\mathrm{m\,s^{-1}} \times 5\times10^{-8}\,\mathrm{T} = 15\,\mathrm{V\,m^{-1}} \)
For the direction, take the wave along \( +z \) and \( \vec{B} \) along \( +y \). The direction of propagation \( \vec{E}\times\vec{B} \) must be \( +\hat{k} \):
\( \displaystyle \hat{\imath}\times\hat{\jmath} = \hat{k} \)
so \( \vec{E} \) is along \( +\hat{\imath} \), the +X axis.