Force acting on dipole in non-uniform electric field

If an electric dipole is positioned in a spatially non-uniform electric field, the forces acting on the point charges that compose the dipole no longer cancel each other and the dipole experiences an overall non-zero acceleration.

Notes:

1. A more general representation of this law, which does not require choosing an axis aligned with the dipole, assuming Cartesian coordinates:

   \[\vec F = \left( \vec p, \nabla \right) \vec E = p_x \frac{\partial \vec E}{\partial x} + p_y \frac{\partial \vec E}{\partial y} + p_z \frac{\partial \vec E}{\partial z}\]

Links:

1. Physics Bootcamp.

force

force acting on the dipole.

Symbol:

F

Latex:

\({\vec F}\)

Dimension:

force

electric_dipole_moment

Magnitude of the electric_dipole_moment vector.

Symbol:

p

Latex:

\(p\)

Dimension:

charge*length

position

position along the axis whose direction is aligned with that of the electric_dipole_moment vector.

Symbol:

x

Latex:

\(x\)

Dimension:

length

electric_field

Vector of the electric field as a function of position. See electric_field_strength.

Symbol:

E(x)

Latex:

\({\vec E} \left( x \right)\)

Dimension:

voltage/length

law

F = p * Derivative(E(x), x)

Latex:

\[{\vec F} = p \frac{d}{d x} {\vec E} \left( x \right)\]