Electric dipole moment of electrically neutral system
=====================================================

The electric dipole moment of an electrically neutral system of (point) charges can be found as
the sum of the products of the values and the position vectors of the charges that compose the
system.

**Notes:**

#. This law can be seen as the definition of electric dipole moment.

#. The value of the electric dipole moment for such a system is independent of the choice of the
   origin of the coordinate frame (i.e. it is translationally invariant).

..
    TODO: derive this property of the electric dipole moment vector

**Conditions:**

#. The system is electrically neutral.

**Links:**

#. `Wikipedia, derivable from the third equation <https://en.wikipedia.org/wiki/Electric_dipole_moment#Expression_(general_case)>`__.

.. py:currentmodule:: symplyphysics.electromagnetism.electrostatics.electric_dipole.electric_dipole_moment_of_electrically_neutral_system

.. py:data:: electric_dipole_moment

    Vector of the :attr:`~symplyphysics.symbols.electrodynamics.electric_dipole_moment` of the system of charges.

Symbol:
    :code:`p`

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

Dimension:
    :code:`charge*length`


.. py:data:: charge

    Value of the :math:`i`-th point charge.

Symbol:
    :code:`q[i]`

Latex:
    :math:`{q}_{i}`

Dimension:
    :code:`charge`


.. py:data:: position_vector

    Position vector of the :math:`i`-th point charge. See :attr:`~symplyphysics.symbols.classical_mechanics.distance_to_origin`.

Symbol:
    :code:`r[i]`

Latex:
    :math:`{{\vec r}}_{i}`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`p = Sum(q[i] * r[i], i)`


    Latex:
        .. math::
            {\vec p} = \sum_i {q}_{i} {{\vec r}}_{i}


.. py:data:: electric_neutrality_condition

    :code:`Sum(q[i], i) = 0`


    Latex:
        .. math::
            \sum_i {q}_{i} = 0