Why light exerts pressure on a metal surface

[Eric Wright]

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

 

[rude man]

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!