prove grad(a.grad(r^-1))= -curl(a cross grad (r^-1))
curl(a x b)= (b dot grad)a - (a dot grad)b +a(div b) - b(div a )
The Attempt at a Solution
Im trying to use index notation and get
di (aj (grad(r^-1))j)
=grad(r^-1) di(aj) +aj(di grad(r^-1))j
which is obviously not right. Ive tried attacking the problem from the reverse direction and haven't had much luck there either.
Thank you :)