Magnetic flux density of linear conductor of finite length¶

Let there be a rectilinear conductor of finite length. Then its magnetic flux density will depend on the magnitude of the current and the material. It also depends on the perpendicular distance to the conductor and on the angles between the lines drawn from the ends of the conductor to the point and the conductor.

Conditions:

Conductor should be rectilinear.
Length of the conductor is finite.

magnetic_flux_density¶: magnetic_flux_density through the conductor.

Symbol:: B
Latex:: \(B\)
Dimension:: magnetic_density

absolute_permeability¶: absolute_permeability of the medium.

Symbol:: mu
Latex:: \(\mu\)
Dimension:: inductance/length

current¶: current running through the conductor.

Symbol:: I
Latex:: \(I\)
Dimension:: current

first_angle¶: angle between origin and the first end of the conductor.

Symbol:: phi_1
Latex:: \(\varphi_{1}\)
Dimension:: angle

second_angle¶: angle between origin and the second end of the conductor.

Symbol:: phi_2
Latex:: \(\varphi_{2}\)
Dimension:: angle

distance¶: Perpendicular euclidean_distance to the conductor.

Symbol:: d
Latex:: \(d\)
Dimension:: length

law¶

B = mu * I * (cos(phi_1) + cos(phi_2)) / (4 * pi * d)

Latex:: \[B = \frac{\mu I \left(\cos{\left(\varphi_{1} \right)} + \cos{\left(\varphi_{2} \right)}\right)}{4 \pi d}\]