An electron is constrained to move along
the y-axis with a speed of 0.1 c (c is the
speed of light) in the presence of
electromagnetic wave, whose electric
field is
$$\overrightarrow E = 30\widehat j\sin \left( {1.5 \times {{10}^7}t - 5 \times {{10}^{ - 2}}x} \right)$$ V/m.
The maximum magnetic force experienced by
the electron will be :
(given c = 3 $\times$ 108 ms–1 and electron charge =
1.6 $\times$ 10–19 C)
Solution
$$
\overrightarrow E = 30\widehat j\sin (1.5 \times {10^7}t - 5 \times {10^{ - 2}}x)V/m$$
<br><br>V = ${{1.5 \times {{10}^2}} \over {5 \times {{10}^{ - 2}}}}$ = 3 $\times$ 10<sup>8</sup> = C
<br><br>$$ \Rightarrow B = E/C = {{30} \over {1.5 \times {{10}^7}}} \times 5 \times {10^{ - 2}}$$<br><br>$= {10^{ - 7}}Tesla$<br><br>$$ \Rightarrow {F_{max}} = q\left( {\overrightarrow V \times \overrightarrow B } \right) = \left| {qVB} \right|$$<br><br>$= 1.6 \times {10^{ - 19}} \times 0.1 \times 3 \times {10^8} \times {10^{ - 7}}$<br><br>$= 4.8 \times {10^{ - 19}}N$
About this question
Subject: Physics · Chapter: Electromagnetic Waves · Topic: Properties of EM Waves
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