Suppose that the electric field part of an electromagnetic wave in vacuum is E = {(3.1 N/C) cos [(1.8 rad/m) y + (5.4 × 10⁶ rad/s)t]} $\hat{i} .$ Write an expression for the magnetic field part of the wave.

Solution

Electric field E = {(3.1 N/C) cos [(1.8 rad/m) y + (5.4 × 10⁶ rad/s)t] $\overset{⏞}{i}$

Expression of magnetic field part of the wave
$B = B_{0} \cos (ky + ωt) = 1.03 \times 10^{- 8} \cos \{(1.8 rad / m) y + (5.4 \times 10^{6} rad / s) t\}$

E is along $\hat{i}$ and c is along $- \overset{⏜}{j}$ ,
c is the direction of $\vec{E} \times \vec{B}$
$- \hat{j} = \hat{i} \times ?$
Clearly B is in the direction of $\hat{k} (\hat{k} \times \hat{i} = \hat{j})$ and $(\hat{i} \times \hat{k} = - \hat{j})$
Thus,
$\vec{B}$ is completely represented as,

$\vec{B} = 1.03 \times 10^{- 8} \cos \{(1.8 rad / m) y + (5.4 \times 10^{6} rad / s) t\} \hat{k} .$

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Suppose that the electric field part of an electromagnetic wave in vacuum is E = {(3.1 N/C) cos [(1.8 rad/m) y + (5.4 × 10⁶ rad/s)t]} $\hat{i} .$ Write an expression for the magnetic field part of the wave.

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Suppose that the electric field part of an electromagnetic wave in vacuum is E = {(3.1 N/C) cos [(1.8 rad/m) y + (5.4 × 10⁶ rad/s)t]} $\hat{i} .$ Write an expression for the magnetic field part of the wave.