Question

The electric field of an electromagnetic wave in free space is represented as $\vec{E} = E_0 \cos(\omega t - kz) \hat{i}$. The corresponding magnetic induction vector will be:

• A. $\vec{B} = E_0 C \cos(\omega t - kz) \hat{j}$
• B. $\vec{B} = \frac{E_0}{C} \cos(\omega t - kz) \hat{j}$
• C. $\vec{B} = E_0 C \cos(\omega t + kz) \hat{j}$
• D. $\vec{B} = \frac{E_0}{C} \cos(\omega t + kz) \hat{j}$

Answer 1

Answer: (B)

$\vec{B} = \frac{E_0}{C} \cos(\omega t - kz) \hat{j}$

Answer 2

Since $\vec{B} = \frac{\vec{E}}{C} \times \hat{k}$:

$\vec{B} = \frac{E_0}{C} \cos(\omega t - kx) \hat{j}$