The electric fields of two plane electromagnetic plane waves in vacuum are given by E→$$1=E0j^$$ $$cos$$ ωt−$$kx$$ and E→$$2=E0k^$$ $$cos$$ ωt−ky. At $$t=0$$ , a particle of charge q is at origin with a velocity v→$$=0.8$$ $$cj^$$ (c$$ is the speed of light in $$vacuum). The instantaneous force experienced by the particle is :

Question

The electric fields of two plane electromagnetic plane waves in vacuum are given by E→$$1=E0j^$$ $$cos$$ ωt−$$kx$$   and  E→$$2=E0k^$$  $$cos$$ ωt−ky. At  $$t=0$$ , a particle of charge q is at origin with a velocity  v→$$=0.8$$ $$cj^$$ (c$$ is the speed of light in $$vacuum). The instantaneous force experienced by the particle is :

Infinity Learn · Accepted Answer

For $$E1$$→  corresponding  $$B1$$→$$=E0Ck^$$  $$cos$$  ωt−kxFor $$E2$$→  corresponding   $$B2$$→$$=E0Ci^$$  $$cos$$  ωt−ky Total force acting at $$t=0$$, $$x=0$$ is​F→$$net=qE$$→$$net+qv$$→×B→net​here​E→net $$=E$$→$$1+E$$→$$2=E0j^+E0k^$$​andB→net $$=B$$→$$1+B$$→$$2=E0Ck^+E0Ci^$$⇒F→ $$=qE0j^+E0k^$$ $$+q0.8$$ $$cj^$$×$$E0Ck^+E0Ci^$$⇒F→ $$=qE0j^+qE0k^+0.8qE0i^$$−$$0.8qE0k^$$​⇒F→$$=qE00.8i^+j^+0.2k^$$

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