F = del(p.E) and F = (p.del)E are equivalent

[izzy93]

Question: In the electrostatic case, the expressions F = del(p.E) and F = (p.del)E are equivalent:

I am having trouble with how to show they are equivalent

In the second equation, I expanded it out to give F= px (dE/dx) + py (dE/dy) + pz(dE/dz)

Any help as to how to do this would be much appreciated

thanks

 

[Meir Achuz]

You have to use the vector differential operator equation
$$\nabla({\bf p\cdot E)=p\times(\nabla\times E)+(p\cdot\nabla)E}$$,
and curl E=0.