- #1
flame_m13
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Homework Statement
Prove vector identity [tex]\nabla[/tex] x[tex]\nabla\phi[/tex] = 0 using index notation.
Homework Equations
[tex]\nabla[/tex] x A = Ejrt[tex]\partial[/tex]rAt
The Attempt at a Solution
I'm treating this as [tex]\nabla[/tex]x A, where A = del [tex]\Phi[/tex] = Etpq[tex]\partial[/tex]p[tex]\Phi[/tex]q
putting A back in the equation:
= EjrtEtpq[tex]\partial[/tex]r[tex]\partial[/tex]p[tex]\Phi[/tex]q
=EtrjEtpq[tex]\partial[/tex]r[tex]\partial[/tex]p[tex]\Phi[/tex]q
=([tex]\partial[/tex]jp[tex]\partial[/tex]rq - [tex]\partial[/tex]jq[tex]\partial[/tex]rp)[tex]\partial[/tex]r[tex]\partial[/tex]p[tex]\Phi[/tex]q
It's here that I'm stuck. I know it should be simple after this, and somehow I need to get zero, but I'm completely stuck. Maybe I messed up somewhere?