Vector Analysis Har Problem

kolahal_b

10th May 2007 - 03:20 PM

A vector field V is not irrotational.Show that it is always possible to find f such that fV is irrotational.

delx[fV]=f*delxV-Vx grad f

V is not irrotational means:

curl(V)=U,say,where U non equal to zero.

f V irrotational means:
curl(fV)=0

curl(fV)=grad(f)xV+f curl(V)=grad(f)xV+f U

So you get:

grad(f)xV+f U=0
grad(f)/f xV+ U=0
grad(ln(f))xV=-U

What to do after that?

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