I'm going to explain my understanding about a bit of a contradiction I can't resolve, and I was hoping somebody could help me understand it. Sorry about the bombardment of vector components! There appears to be two methods we can use to calculate the force (effectively the same in fact, but one is a bit of a shortcut): 1. Find the potential energy of the dipole using U=-p.E =-pxEx-pyEy-pzEz. Then simply use F=-∇U to get the force. This comes out as F=(px∂Ex/∂x+py∂Ey/∂x+pz∂Ez/∂x)i+(px∂Ex/∂y+py∂Ey/∂y+pz∂Ez/∂y)j+(px∂Ex/∂z+py∂Ey/∂z+pz∂Ez/∂z)k Now this method has given me correct answers when I have started with a specific vector function E, found its corresponding U and then got F 2. The 'shortcut'. We can use a vector calculus identity so that F=-∇U=-∇(-p.E)=∇(p.E)=(p.∇)E. All this means is we can find F without the intermediate stage of needing U. All we need is E. However this in component form gives F=(px∂Ex/∂x+py∂Ex/∂y+pz∂Ex/∂z)i+(px∂Ey/∂x+py∂Ey/∂y+pz∂Ey/∂z)j+(px∂Ez/∂x+py∂Ez/∂y+pz∂Ez/∂z)k So the same vector F comes out in two different ways. Now, I can't find any reason that makes them equal, but I recall using the first correctly for a specific field, and the second method I'm assuming would have given me the correct answer too, so why aren't they agreeing with one another for a general dipole in a general field in component form? Thanks for any help!