Magnetic field due to current loop along axis¶

Using the Biot—Savart law, we can calculate the magnetic field due to a current loop along its axis of symmetry. The magnetic field is directed along that axis, is proportional to the current in the loop and depends on the distance to the center of the loop and the radius of the loop.

Conditions:

The medium is vacuum.

Links:

Physics LibreTexts — Magnetic Field of a Current Loop.

magnetic_flux_density¶: Radial component (i.e. along the axis of the loop) of the magnetic_flux_density vector.

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

current¶: Electric current in the loop.

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

loop_radius¶: radius of the loop.

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

distance¶: euclidean_distance from the point at which the magnetic field is measured to the center of the loop.

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

law¶

B = mu_0 * I * r^2 / (2 * (d^2 + r^2)^(3/2))

Latex:: \[B = \frac{\mu_0 I r^{2}}{2 \left(d^{2} + r^{2}\right)^{\frac{3}{2}}}\]