The electric fields of two plane electromagnetic plane waves in vacuum are given by E 1 → = E 0 j ^ cos ⁡ ω t - k x and E 2 → = E 0 k ^ cos ⁡ ω t - k y At t = 0 , a particle of charge q is at origin w

Question

The electric fields of two plane electromagnetic plane waves in vacuum are given by E 1 → = E 0 j ^ cos ⁡ ω t - k x and E 2 → = E 0 k ^ cos ⁡ ω t - k y At t = 0 , a particle of charge q is at origin with a velocity v → = 08 c j ^ ( c is the speed of light in vaccum). The instantaneous force experienced by the particle is:

TestHub · Accepted Answer

Magnetic field vectors associated with this electromagnetic wave are given by
${\vec{B}}_{1} = \frac{E_{0}}{c} \hat{k} \cos (k x - ω t)$ & ${\vec{B}}_{2} = \frac{E_{0}}{c} \hat{i} \cos (k y - ω t)$
$\vec{F} = q \vec{E} + q (\vec{V} \times \vec{B})$
$= q ({\vec{E}}_{1} + {\vec{E}}_{2}) + q (\vec{V} \times ({\vec{B}}_{1} + {\vec{B}}_{2}))$
By putting the value of ${\vec{E}}_{1}, {\vec{E}}_{2}, {\vec{B}}_{1} & {\vec{B}}_{2}$
The net Lorentz force on the charged particles is
$\vec{F} = q E_{0} [0.8 \cos (k x - ω t) \hat{i} + c o s (k y - ω t) \hat{j} + 0.2 c o s (k y - ω t) \hat{k}]$
At $t = 0$ and at $x = y = 0$
$\vec{F} = q E_{0} [0.8 \hat{i} + \hat{j} + 0.2 \hat{k}]$

Physics - EM Waves Question with Solution | TestHub

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