Solving Vector Identity: {phi (grad phi)} X (n^)dS=0

AI Thread Summary
The discussion focuses on proving that the closed integral of the expression {phi (grad phi)} X (n^)dS equals zero. Participants clarify that 'X' denotes the cross product between the normal vector and the gradient. The divergence theorem is suggested as a key tool for the proof. A specific approach using the relationship between surface integrals and volume integrals is recommended, specifically \int_S n \times a dS = \int_V curl(a) dV. This guidance aims to assist in solving the problem effectively.
Kolahal Bhattacharya
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Homework Statement



I am to show: closed integral {phi (grad phi)} X (n^)dS=0

Homework Equations





The Attempt at a Solution



I understand I am to use divergence theorem here.but cannot approach.Please help
 
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Is 'X' supposed to mean a cross product between the normal vector and the gradient?
 
yes.It means that.
 
Try using \int_S n \times a dS = \int_V curl(a) dV.
 
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