# Force on an electric dipole

The PE of an electric dipole in an external

U=-

where

**E**-field isU=-

**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

F_{x}=p_{x}∂E_{x}/∂x+p_{y}∂E_{y}/∂x+p_{z}∂E_{z}/∂x

F_{y}=p_{x}∂E_{x}/∂y+p_{y}∂E_{y}/∂y+p_{z}∂E_{z}/∂y

F_{z}=p_{x}∂E_{x}/∂z+p_{y}∂E_{y}/∂z+p_{z}∂E_{z}/∂z

however my book annoyingly states that these should be

F_{x}=p_{x}∂E_{x}/∂x+p_{y}∂E_{x}/∂y+p_{z}∂E_{x}/∂z

F_{y}=p_{x}∂E_{y}/∂x+p_{y}∂E_{y}/∂y+p_{z}∂E_{y}/∂z

F_{z}=p_{x}∂E_{z}/∂x+p_{y}∂E_{z}/∂y+p_{z}∂E_{z}/∂z

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

http://ift.tt/PszmPk

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