Given divergence and curl determine vector field

[akshay.wizard]

the divergence and the curl of a vector field "A" are specified everywhere in a volume V. The normal component of curl A is also specified on the surface S bounding V. Show that these data enable one to determine the vector field in the region

 

[henry_m]

Try taking the curl of the curl...

(BTW, I think you can only work out the field up to a constant)

 

[l470594464]

Use the formula:\Delta\vec{A}=\nabla(\nabla\bullet\vec{A})-\nabla\times(\nabla\times\vec{A}). You'll get three Laplace equation about P,Q,R.Assume \vec{A}=(P,Q,R).\Deltameans twice \nabla.