Maxwell Stress Tensor: Application & Force Calculation

[Hassan2]

Hello everyone,

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

 

[eljose79]

Dear Hassan,

Thank you for your question about the application of Maxwell stress tensor. The confusion you have mentioned is a common one and I would be happy to clarify it for you.

The Maxwell stress tensor is a mathematical tool used to calculate the electromagnetic force on a body. It is derived from the Maxwell equations, which describe the behavior of electromagnetic fields. The formula for calculating the force on a body involves a surface integral, which means the surface must completely enclose the body in question. This is because the force is calculated by considering the interactions between the electromagnetic field and the surface of the body.

Now, regarding the condition of the body being surrounded by air, this is not a necessary condition for the application of the Maxwell stress tensor. The body can be surrounded by any medium, as long as the surface used for the integral encloses the body completely. In the problem you mentioned, the northern hemisphere of the sphere is used as a surface for the integral, which still encloses the entire sphere.

I hope this clarifies your confusion. If you have any further questions, please feel free to ask. As scientists, it is important to question and seek clarification in order to fully understand concepts and their applications.