Question 31

For an electromagnetic wave propagating through vacuum, $$\vec{k}$$, $$\vec{E}$$ and $$\omega$$ represent propagation vector, electric field and angular frequency, respectively. The magnetic field associated with this wave is represented by :

$$\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$$

$$\nabla \times \vec{E} = \vec{k} \times \vec{E}$$

$$-\frac{\partial \vec{B}}{\partial t} = \omega \vec{B}$$

$$\vec{k} \times \vec{E} = \omega \vec{B}$$

$$\vec{B} = \frac{\vec{k} \times \vec{E}}{\omega}$$

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