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:**

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

   .. math::

       \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:**

#. `Physics Bootcamp <https://www.physicsbootcamp.org/Torque-on-an-Electric-Dipole.html>`__.

.. py:currentmodule:: symplyphysics.laws.electricity.vector.force_acting_on_dipole_in_non_uniform_electric_field

.. py:data:: force

    :attr:`~symplyphysics.symbols.classical_mechanics.force` acting on the dipole.

Symbol:
    :code:`F`

Latex:
    :math:`{\vec F}`

Dimension:
    :code:`force`


.. py:data:: electric_dipole_moment

    Magnitude of the :attr:`~symplyphysics.symbols.electrodynamics.electric_dipole_moment` vector.

Symbol:
    :code:`p`

Latex:
    :math:`p`

Dimension:
    :code:`charge*length`


.. py:data:: position

    :attr:`~symplyphysics.symbols.classical_mechanics.position` along the axis whose direction is aligned with that of the
    :attr:`~electric_dipole_moment` vector.

Symbol:
    :code:`x`

Latex:
    :math:`x`

Dimension:
    :code:`length`


.. py:data:: electric_field

    Vector of the electric field as a function of :attr:`~position`. See
    :attr:`~symplyphysics.symbols.electrodynamics.electric_field_strength`.

Symbol:
    :code:`E(x)`

Latex:
    :math:`{\vec E} \left( x \right)`

Dimension:
    :code:`voltage/length`


.. py:data:: law

    :code:`F = p * Derivative(E(x), x)`


    Latex:
        .. math::
            {\vec F} = p \frac{d}{d x} {\vec E} \left( x \right)