The magnetic field of an E.M. wave is given by:
\[
\vec{B} = \left( \frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j} \right) 30 \sin \left( \omega \left( t - \frac{z}{c} \right) \right)
\]
The corresponding electric field in S.I. units is:
Show Hint
For an electromagnetic wave, the electric and magnetic fields are perpendicular and related through the speed of light.
The relationship between the magnetic field \( \vec{B} \) and electric field \( \vec{E} \) in an electromagnetic wave is described by the equation \( \vec{E} = \vec{B} \times \hat{c} \), and also by \( \vec{E} = B_0 c \), where \( c \) represents the speed of light.
The given magnetic field is:
\[
\vec{B} = \left( \frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j} \right) 30 \sin \left( \omega \left( t - \frac{z}{c} \right) \right)
\]
The electric field \( \vec{E} \) is computed using the cross product and the relation \( \vec{E} = B_0 c \). The resultant electric field is:
\[
\vec{E} = \left( \frac{1}{2} \hat{i} - \frac{\sqrt{3}}{2} \hat{j} \right) 30 c \sin \left( \omega \left( t - \frac{z}{c} \right) \right)
\]
