Electromagnetic force calculation

[krindik]

Hi,

I understand that force due to an electromagnetic field on a surface can be calculated by
$$F = \oint {T . n dS}$$ where $$T$$ is Maxwell stress tensor.
http://en.wikipedia.org/wiki/Maxwell_stress_tensor"

And this tensor consists of $$E_x, E_y, E_z, H_x, H_y, H_z$$

I don't understand how the field points are used in the force calculation, say for example, to calculate force on a dielectric sphere in an EM wave in vacuum.

What are field points used for E_x, ..., H_x, ... ? Are the within the dielectric or in vacuum?
Since the fields on the boundary are not known (only fields in either side of the boundary are known) how do you calculate the force?

Can somebody shed some light on this or point me to some example where a similar calculation is done?

Thanks in advance

 

[TMM]

Forces on surfaces are always (as far as I've seen) calculated using the average field.

 

[krindik]

Thanks. Can u point me to some text or online notes where it uses the averaging method?

 

[TMM]

I learned that method of calculating force from Griffith's Introduction to Electrodynamics. He also has a section in chapter 8 discussing the stress tensor. He describes the reasoning for the average is that it eliminates the surface's own field (which is locally symmetric due to Gauss' Law and Ampere's Law) which doesn't exert a force on itself.