Force on an electric dipole

The PE of an electric dipole in an external E-field is
U=-p.E
where p is it’s dipole moment.

I was under the impression I could find U, and then easily determine the force on the dipole using F=-∇U, to obtain
Fx=px∂Ex/∂x+py∂Ey/∂x+pz∂Ez/∂x
Fy=px∂Ex/∂y+py∂Ey/∂y+pz∂Ez/∂y
Fz=px∂Ex/∂z+py∂Ey/∂z+pz∂Ez/∂z

however my book annoyingly states that these should be

Fx=px∂Ex/∂x+py∂Ex/∂y+pz∂Ex/∂z
Fy=px∂Ey/∂x+py∂Ey/∂y+pz∂Ey/∂z
Fz=px∂Ez/∂x+py∂Ez/∂y+pz∂Ez/∂z

which they give a derivation for in a different way. However they do go on to prove later that FL=-∂U/∂L with L the direction in question. I’m now very confused.

http://ift.tt/PszmPk

Leave a comment

Your email address will not be published.


*


Show Buttons
Hide Buttons