We know that the force acting on the area element dS of a conductor is,
![](https://www.sarthaks.com/?qa=blob&qa_blobid=9662618597473554137)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=9735286918955347777)
It follows from symmetry considerations that the resultant force vector F directed along the z-axis, and hence it can be represented as the sum (integral) of the projection of elementary forces (1) onto the z-axis :
![](https://www.sarthaks.com/?qa=blob&qa_blobid=9141094980739138536)
For simplicity let us consider an element area
![](https://www.sarthaks.com/?qa=blob&qa_blobid=6110774274174141870)
Integrating this expression over the half sphere (i.e. with respect to cosθ between 1 and 0), we obtain
![](https://www.sarthaks.com/?qa=blob&qa_blobid=13315883497464745106)