Electrostatic force between two charges
=======================================

Also known as **Coulomb's law**, it is an experimental law that calculates the amount
of force between two electrically charged particles at rest.

Also see the :ref:`scalar law <Electrostatic force via charges and distance>`.

**Notes:**

#. If a given charge is in the vicinity of a system of point charges, then the net law can be
   found via the :ref:`principle of superposition <Superposition of forces is sum (Vector)>`.

**Notation:**

#. :math:`\varepsilon_0` (:code:`epsilon_0`) is :attr:`~symplyphysics.quantities.vacuum_permittivity`.

**Conditions:**

#. The charges are small.

#. The charges are at rest.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Coulomb%27s_law#Mathematical_form>`__.

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

.. py:data:: force

    Vector of the electrostatic :attr:`~symplyphysics.symbols.classical_mechanics.force` experienced by the :attr:`~first_charge` in the
    vicinity of the :attr:`~second_charge` in vacuum.

Symbol:
    :code:`F_12`

Latex:
    :math:`{\vec F}_{12}`

Dimension:
    :code:`force`


.. py:data:: first_charge

    Value of the first point :attr:`~symplyphysics.symbols.electrodynamics.charge`.

Symbol:
    :code:`q_1`

Latex:
    :math:`q_{1}`

Dimension:
    :code:`charge`


.. py:data:: second_charge

    Value of the second point :attr:`~symplyphysics.symbols.electrodynamics.charge`.

Symbol:
    :code:`q_2`

Latex:
    :math:`q_{2}`

Dimension:
    :code:`charge`


.. py:data:: position_vector

    Position vector drawn from the :attr:`~second_charge` to the :attr:`~first_charge`.

Symbol:
    :code:`d_21`

Latex:
    :math:`{\vec d}_{21}`

Dimension:
    :code:`length`


.. py:data:: force_law

    :code:`F_12 = q_1 * q_2 / (4 * pi * epsilon_0) * d_21 / norm(d_21)^3`


    Latex:
        .. math::
            {\vec F}_{12} = \frac{q_{1} q_{2}}{4 \pi \varepsilon_0} \frac{{\vec d}_{21}}{\left \Vert {\vec d}_{21} \right \Vert^{3}}


.. py:data:: position_vector_law

    :code:`d_21 = sign(q_1 * q_2) * sqrt(Abs(q_1 * q_2) / (4 * pi * epsilon_0)) * F_12 / norm(F_12)^(3/2)`


    Latex:
        .. math::
            {\vec d}_{21} = \operatorname{sign}{\left(q_{1} q_{2} \right)} \sqrt{\frac{\left|{q_{1} q_{2}}\right|}{4 \pi \varepsilon_0}} \frac{{\vec F}_{12}}{\left \Vert {\vec F}_{12} \right \Vert^{\frac{3}{2}}}