(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Wangsness Exercise 24-6

A particle of charge q and mass m is travelling with a velcoity u i nthe field of a plane EM wave in free space that itself is travelling in the z direction.

Find the force on the particle.

What does this become for the special case in whic hthe particle is travelling in the same direction as teh wave?

What is the direction of the force?

Under what circumstances (if any) will the force vanish in this case??

2. The attempt at a solution

First of all im stumped as how to find the force. Would i just simply use the lorentz force law??

If that is the case then

Suppose we assume the E to point in teh X direction and the B to point in teh Y direction then

[tex] \vec{F} = q (\vec{E} + \vec{u} \times \vec{B}) [/tex]

suppose the particle was travelling in teh Z direction then

[tex] \vec{F} = q (\vec{E} + u\hat{z} \times B\hat{y} ) [/tex]

[tex] \vec{F} = q (\vec{E} + uB (-\hat{x})) [/tex]

the force is pointing the x direction

The magnetic force would vanish if V is parallel to B

but the electric force will never vanish

is this even clseo to being right? OR am i sorely mistaken?

Thanks for your input!

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# A particle and a wave

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