Why light exerts pressure on a metal surface

Eric Wright
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Homework Statement



By considering the E and B fields of an incident monochromatic plane wave on a metal surface, as well as the current density of mobile electrons, J and the resulting EM force F felt by them, show that there is a force on the metal due to the magnetic force on the mobile electrons.

Homework Equations



\vec F = q( \vec E + \vec v \times \vec B )

\vec E = E_0 e^{ky-wt} \hat k

\vec B = \frac{E_0}{c} e^{ky-wt} \hat i


The Attempt at a Solution



Let the surface be the zy plane. Then at the surface we have

\vec E = E_0 e^{-wt} \hat k
\vec B = \frac{E_0}{c} e^{-wt} \hat i

Consider a mobile electron on the surface. The E field will cause the electron to move in the -z direction. Then since the electron is now moving, the B field will exert a force in the
- \hat k \times \hat i = \hat j
direction. Applying this to all mobile electrons we get a net force in the y direction on the surface.

I just wanted to see if my logic here is correct.. Am I missing any important details?

Any reply would be great.. thanks!

Eric
 
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Eric Wright said:

Homework Statement



By considering the E and B fields of an incident monochromatic plane wave on a metal surface, as well as the current density of mobile electrons, J and the resulting EM force F felt by them, show that there is a force on the metal due to the magnetic force on the mobile electrons.

Homework Equations



\vec F = q( \vec E + \vec v \times \vec B )

\vec E = E_0 e^{ky-wt} \hat k

\vec B = \frac{E_0}{c} e^{ky-wt} \hat i


The Attempt at a Solution



Let the surface be the zy plane. Then at the surface we have

\vec E = E_0 e^{-wt} \hat k
\vec B = \frac{E_0}{c} e^{-wt} \hat i

Consider a mobile electron on the surface. The E field will cause the electron to move in the -z direction. Then since the electron is now moving, the B field will exert a force in the
- \hat k \times \hat i = \hat j
direction. Applying this to all mobile electrons we get a net force in the y direction on the surface.

I just wanted to see if my logic here is correct.. Am I missing any important details?

Any reply would be great.. thanks!

Eric

Looks right to me!
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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