First slide

Introduction-Electromagnetic waves

Question

The electric field of a plane electromagnetic wave is given by $\vec{E} = E_{0} (\hat{x} + \hat{y}) \sin (k z - ω t)$ . Its magnetic field will be given by

Moderate

A

$\frac{E_{0}}{c} (\hat{x} + \hat{y}) \sin (k z - ω t)$
B

$\frac{E_{0}}{c} (- \hat{x} + \hat{y}) \sin (k z - ω t)$
C

$\frac{E_{0}}{c} (\hat{x} - \hat{y}) \sin (k z - ω t)$
D

$\frac{E_{0}}{c} (\hat{x} - \hat{y}) \cos (k z - ω t)$

Solution

$\begin{array}{l} \vec{B} will have same phase as \bar{E} \\ \hat{B} = \hat{C} \times \hat{E} = \hat{z} \times (\hat{x} + \hat{y}) = (\hat{y} - \hat{x}) \\ Also, B_{0} = \frac{E_{0}}{C} \\ ∴ \vec{B} = \frac{E_{0}}{C} (- \hat{x} + \hat{y}) \sin (kz - ω t) \end{array}$

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