For a plane electromagnetic wave, the magnetic field at a point x and time t is
$\overrightarrow B \left( {x,t} \right)$ = $$\left[ {1.2 \times {{10}^{ - 7}}\sin \left( {0.5 \times {{10}^3}x + 1.5 \times {{10}^{11}}t} \right)\widehat k} \right]$$ T
The instantaneous electric field $\overrightarrow E$
corresponding to $\overrightarrow B$
is :
(speed of light c = 3 × 108
ms–1)
Solution
Given,
<br>$\overrightarrow B \left( {x,t} \right)$ = $$\left[ {1.2 \times {{10}^{ - 7}}\sin \left( {0.5 \times {{10}^3}x + 1.5 \times {{10}^{11}}t} \right)\widehat k} \right]$$ T
<br><br>Wave is travelling along (–x) axis and $\overrightarrow B$ is along
+z axis.
<br><br>We know, Magnitude of electric field
<br><br>E = BC
<br><br>= 1.2 $\times$ 10<sup>-7</sup> sin ( 0.5 10 + 1.5$\times$10<sup>11</sup>t ) $\times$ 3 $\times$ 10<sup>8</sup>
<br><br>= 36 sin (0.5$\times$10<sup>3</sup>x+1.5$\times$10<sup>11</sup>t) V/m
<br><br>Also, $$\overrightarrow s = {{\overrightarrow E \times \overrightarrow B } \over {{\mu _0}}}$$
<br><br>$\Rightarrow$ $- \widehat i = {{\overrightarrow E \times \widehat k} \over {{\mu _0}}}$
<br><br>$\therefore$ Direction of ${\overrightarrow E = - \widehat j}$
<br><br>$\therefore$ Instantaneous electric field,
<br><br> $$\overrightarrow E \left( {x,t} \right) = \left[ { - 36\sin \left( {0.5 \times {{10}^3}x + 1.5 \times {{10}^{11}}t} \right)\widehat j} \right]{V \over m}$$
About this question
Subject: Physics · Chapter: Electromagnetic Waves · Topic: Maxwell's Equations
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