Magnetic field due to finite coil along axis
============================================

Using the Biot—Savart law, it is possible to obtain the formula for the magnetic flux density at
any point on the axis of a coil. It is directly proportional to the coil's turn count and current
and inversely proportional to its length, and also depends on the position of the measurement
point relative to the coil ends.

**Conditions:**

#.  The point of measurement must lie on the axis of the coil.

#.  The medium is a vacuum.

#.  The :math:`z`-axis is the axis of rotation and is oriented according to the right-hand side
    rule.

**Links:**

#. `Physics LibreTexts — Solenoids and Toroids. Equation (12.7.4) <https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)/12%3A_Sources_of_Magnetic_Fields/12.07%3A_Solenoids_and_Toroids>`__.

.. py:currentmodule:: symplyphysics.laws.electricity.magnetic_field_due_to_finite_coil_along_axis

.. py:data:: magnetic_flux_density

    Magnitude of :attr:`~symplyphysics.symbols.electrodynamics.magnetic_flux_density`.

Symbol:
    :code:`B`

Latex:
    :math:`B`

Dimension:
    :code:`magnetic_density`


.. py:data:: current

    :attr:`~symplyphysics.symbols.electrodynamics.current` flowing through the wire.

Symbol:
    :code:`I`

Latex:
    :math:`I`

Dimension:
    :code:`current`


.. py:data:: turn_count

    Number of turns in the coil. See :attr:`~symplyphysics.symbols.basic.positive_number`.

Symbol:
    :code:`N`

Latex:
    :math:`N`

Dimension:
    :code:`dimensionless`


.. py:data:: coil_length

    :attr:`~symplyphysics.symbols.classical_mechanics.length` of the coil.

Symbol:
    :code:`l`

Latex:
    :math:`\ell`

Dimension:
    :code:`length`


.. py:data:: first_angle

    Acute :attr:`~symplyphysics.symbols.basic.angle` between the coil axis (or side) and the vector from the measuring point and
    the first end of the coil (that has a smaller :math:`z` coordinate).

Symbol:
    :code:`phi_1`

Latex:
    :math:`\varphi_{1}`

Dimension:
    :code:`angle`


.. py:data:: second_angle

    Acute :attr:`~symplyphysics.symbols.basic.angle` between the coil axis (or side) and the vector from the measuring point and
    the second end of the coil (that has a greater :math:`z` coordinate).

Symbol:
    :code:`phi_2`

Latex:
    :math:`\varphi_{2}`

Dimension:
    :code:`angle`


.. py:data:: law

    :code:`B = mu_0 * I * N / (2 * l) * (cos(phi_1) + cos(phi_2))`


    Latex:
        .. math::
            B = \frac{\mu_0 I N}{2 \ell} \left(\cos{\left(\varphi_{1} \right)} + \cos{\left(\varphi_{2} \right)}\right)