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I have a confusion about the application of Maxwell stress tensor:

I have read some materials about Maxwell stress tensor and its application in calculating electromagnetic force on a body. To this end, a closed surface is assumed around the body and a surface integral on this surface gives the total force on the body. Now my problem is that, some materials say the body must be surrounded by air and the closed surface must be in the surrounding air, while the derivation of the formula doesn't say anything about such a condition. Besides, in a problem in http://einstein1.byu.edu/~masong/emsite/S4Q20/S4Q20.html , the force on the northern hemisphere of a sphere is calculated buy assuming the closed surface cutting the sphere into two hemisphere.

Can anyone make this clear to me?

Your help would be highly appreciated.

Regards,

Hassan