magpylib.core package

magpylib.core package#

The core sub-package gives direct access to our field implementations.

magpylib.core.current_circle_field(field: str, observers: ndarray, current: ndarray, diameter: ndarray) → ndarray#

Magnetic field of a circular (line) current loop.

The loop lies in the z=0 plane with the coordinate origin at its center.

Parameters:

field (str, default=`'B'`) – If field=’B’ return B-field in units of mT, if field=’H’ return H-field in units of kA/m.
observers (ndarray, shape (n,3)) – Observer positions (x,y,z) in Cartesian coordinates in units of mm.
current (ndarray, shape (n,)) – Electrical current in units of A.
diameter (ndarray, shape (n,)) – Diameter of loop in units of mm.

Returns:

B-field or H-field – B/H-field of current in Cartesian coordinates (Bx, By, Bz) in units of mT/(kA/m).

Return type:

ndarray, shape (n,3)

Examples

Compute the field of three different loops at three different positions.

>>> import numpy as np
>>> import magpylib as magpy
>>> cur = np.array([1,1,2])
>>> dia = np.array([2,4,6])
>>> obs = np.array([(1,1,1), (2,2,2), (3,3,3)])
>>> B = magpy.core.current_circle_field('B', obs, cur, dia)
>>> print(B)
[[0.06235974 0.06235974 0.02669778]
 [0.03117987 0.03117987 0.01334889]
 [0.04157316 0.04157316 0.01779852]]

Notes

Implementation based on “Numerically stable and computationally efficient expression for the magnetic field of a current loop.”, M.Ortner et al, Submitted to MDPI Magnetism, 2022

magpylib.core.current_line_field(*args, **kwargs)#: current_line_field is deprecated, see current_polyline_field

magpylib.core.current_loop_field(*args, **kwargs)#: current_loop_field is deprecated, see current_circle_field

magpylib.core.current_polyline_field(field: str, observers: ndarray, current: ndarray, segment_start: ndarray, segment_end: ndarray) → ndarray#

Magnetic field of line current segments.

The current flows from start to end positions. The field is set to (0,0,0) on a line segment.

Parameters:

field (str, default=`'B'`) – If field=’B’ return B-field in units of mT, if field=’H’ return H-field in units of kA/m.
observers (ndarray, shape (n,3)) – Observer positions (x,y,z) in Cartesian coordinates in units of mm.
current (ndarray, shape (n,)) – Electrical current in units of A.
start (ndarray, shape (n,3)) – Polyline start positions (x,y,z) in Cartesian coordinates in units of mm.
end (ndarray, shape (n,3)) – Polyline end positions (x,y,z) in Cartesian coordinates in units of mm.

Returns:

B-field or H-field – B/H-field of current in Cartesian coordinates (Bx, By, Bz) in units of mT/(kA/m).

Return type:

ndarray, shape (n,3)

Examples

Compute the field of two segments. The 2nd observer lies on the segment so that [0 0 0] is returned.

>>> import numpy as np
>>> import magpylib as magpy
>>> curr = np.array([1,2])
>>> start = np.array([(-1,0,0), (-1,0,0)])
>>> end   = np.array([( 1,0,0), ( 2,0,0)])
>>> obs   = np.array([( 0,0,1), ( 0,0,0)])
>>> B = magpy.core.current_polyline_field('B', obs, curr, start, end)
>>> print(B)
[[ 0.         -0.14142136  0.        ]
 [ 0.          0.          0.        ]]

Notes

Field computation via law of Biot Savart. See also countless online resources. eg. http://www.phys.uri.edu/gerhard/PHY204/tsl216.pdf

magpylib.core.dipole_field(field: str, observers: ndarray, moment: ndarray) → ndarray#

Magnetic field of a dipole moment.

The dipole moment lies in the origin of the coordinate system.

Parameters:

field (str, default=`'B'`) – If field=’B’ return B-field in units of mT, if field=’H’ return H-field in units of kA/m.
observers (ndarray, shape (n,3)) – Observer positions (x,y,z) in Cartesian coordinates in units of mm.
moment (ndarray, shape (n,3)) – Dipole moment vector in units of mT*mm^3.

Returns:

B-field or H-field – B/H-field of dipole in Cartesian coordinates (Bx, By, Bz) in units of mT/(kA/m).

Return type:

ndarray, shape (n,3)

Examples

Compute the B-field of two different dipole-observer instances.

>>> import numpy as np
>>> import magpylib as magpy
>>> mom = np.array([(1,2,3), (0,0,1)])
>>> obs = np.array([(1,1,1), (0,0,2)])
>>> B = magpy.core.dipole_field('B', obs, mom)
>>> print(B)
[[0.07657346 0.06125877 0.04594407]
 [0.         0.         0.01989437]]

Notes

The field is similar to the outside-field of a spherical magnet with Volume = 1 mm^3.

magpylib.core.magnet_cuboid_field(field: str, observers: ndarray, magnetization: ndarray, dimension: ndarray) → ndarray#

Magnetic field of a homogeneously magnetized cuboid.

The cuboid sides are parallel to the coordinate axes. The geometric center of the cuboid lies in the origin.

Parameters:

field (str, default=`'B'`) – If field=’B’ return B-field in units of mT, if field=’H’ return H-field in units of kA/m.
observers (ndarray, shape (n,3)) – Observer positions (x,y,z) in Cartesian coordinates in units of mm.
magnetization (ndarray, shape (n,3)) – Homogeneous magnetization vector in units of mT.
dimension (ndarray, shape (n,3)) – Cuboid side lengths in units of mm.

Returns:

B-field or H-field – B/H-field of magnet in Cartesian coordinates (Bx, By, Bz) in units of mT/(kA/m).

Return type:

ndarray, shape (n,3)

Examples

Compute the field of three different instances.

>>> import numpy as np
>>> import magpylib as magpy
>>> mag = np.array([(222,333,555), (33,44,55), (0,0,100)])
>>> dim = np.array([(1,1,1), (2,3,4), (1,2,3)])
>>> obs = np.array([(1,2,3), (2,3,4), (0,0,0)])
>>> B = magpy.core.magnet_cuboid_field('B', obs, mag, dim)
>>> print(B)
[[ 0.49343022  1.15608356  1.65109312]
 [ 0.82221622  1.18511282  1.46945423]
 [ 0.          0.         88.77487579]]

Notes

Field computations via magnetic surface charge density. Published several times with similar expressions:

Yang: Superconductor Science and Technology 3(12):591 (1999)

Engel-Herbert: Journal of Applied Physics 97(7):074504 - 074504-4 (2005)

Camacho: Revista Mexicana de Fisica E 59 (2013) 8–17

Avoiding indeterminate forms:

In the above implementations there are several indeterminate forms where the limit must be taken. These forms appear at positions that are extensions of the edges in all xyz-octants except bottQ4. In the vicinity of these indeterminate forms the formula becomes numerically instable.

Chosen solution: use symmetries of the problem to change all positions to their bottQ4 counterparts. see also

Cichon: IEEE Sensors Journal, vol. 19, no. 7, April 1, 2019, p.2509

magpylib.core.magnet_cylinder_field(field: str, observers: ndarray, magnetization: ndarray, dimension: ndarray) → ndarray#

Magnetic field of a homogeneously magnetized cylinder.

The cylinder axis coincides with the z-axis and the geometric center of the cylinder lies in the origin.

Parameters:

field (str, default=`'B'`) – If field=’B’ return B-field in units of mT, if field=’H’ return H-field in units of kA/m.
observers (ndarray, shape (n,3)) – Observer positions (x,y,z) in Cartesian coordinates in units of mm.
magnetization (ndarray, shape (n,3)) – Homogeneous magnetization vector in units of mT.
dimension (ndarray, shape (n,2)) – Cylinder dimension (d,h) with diameter d and height h in units of mm.
observer (ndarray, shape (n,3)) – Observer positions (x,y,z) in Cartesian coordinates in units of mm.
field – If field=’B’ return B-field in units of mT, if field=’H’ return H-field in units of kA/m.

Returns:

B-field or H-field – B/H-field of magnet in Cartesian coordinates (Bx, By, Bz) in units of mT/(kA/m).

Return type:

ndarray, shape (n,3)

Examples

Compute the B-field of two different cylinder magnets at position (1,2,3).

>>> import numpy as np
>>> import magpylib as magpy
>>> mag = np.array([(0,0,1000), (100,0,100)])
>>> dim = np.array([(1,1), (2,3)])
>>> obs = np.array([(1,2,3), (1,2,3)])
>>> B = magpy.core.magnet_cylinder_field('B', obs, mag, dim)
>>> print(B)
[[ 0.77141782  1.54283565  1.10384481]
 [-0.15185713  2.90352915  2.23601722]]

Notes

Axial implementation based on

Derby: American Journal of Physics 78.3 (2010): 229-235.

Diametral implementation based on

Caciagli: Journal of Magnetism and Magnetic Materials 456 (2018): 423-432.

Leitner/Rauber/Orter: WIP

magpylib.core.magnet_cylinder_segment_field(field: str, observers: ndarray, magnetization: ndarray, dimension: ndarray) → ndarray#

Magnetic field of a homogeneously magnetized cylinder segment.

The full cylinder axis coincides with the z-axis of the coordinate system. The geometric center of the full cylinder lies in the origin.

Parameters:

field (str, default=`'B'`) – If field=’B’ return B-field in units of mT, if field=’H’ return H-field in units of kA/m.
observers (ndarray, shape (n,3)) – Observer positions (x,y,z) in Cartesian coordinates in units of mm.
magnetization (ndarray, shape (n,3)) – Homogeneous magnetization vector in units of mT.
dimension (ndarray, shape (n,5)) – Cylinder segment dimensions (r1,r2,h,phi1,phi2) with inner radius r1, outer radius r2, height h in units of mm and the two segment angles phi1 and phi2 in units of deg.

Returns:

B-field or H-field – B/H-field of magnet in Cartesian coordinates (Bx, By, Bz) in units of mT/(kA/m).

Return type:

ndarray, shape (n,3)

Examples

Compute the field of two different cylinder segment magnets at position (1,1,1).

>>> import numpy as np
>>> import magpylib as magpy
>>> mag = np.array([(0,0,100), (50,50,0)])
>>> dim = np.array([(0,1,2,0,90), (1,2,4,35,125)])
>>> obs = np.array([(1,1,1), (1,1,1)])
>>> B = magpy.core.magnet_cylinder_segment_field('B', obs, mag, dim)
>>> print(B)
[[ 6.27410168  6.27410168 -1.20044166]
 [29.84602335 20.75731598  0.34961733]]

Notes

Implementation based on

Slanovc: Journal of Magnetism and Magnetic Materials, 2022 (in review)

magpylib.core.magnet_sphere_field(field: str, observers: ndarray, magnetization: ndarray, diameter: ndarray) → ndarray#

Magnetic field of a homogeneously magnetized sphere.

The center of the sphere lies in the origin of the coordinate system.

Parameters:

field (str, default=`'B'`) – If field=’B’ return B-field in units of mT, if field=’H’ return H-field in units of kA/m.
observers (ndarray, shape (n,3)) – Observer positions (x,y,z) in Cartesian coordinates in units of mm.
magnetization (ndarray, shape (n,3)) – Homogeneous magnetization vector in units of mT.
diameter (ndarray, shape (n,3)) – Sphere diameter in units of mm.

Returns:

B-field or H-field – B/H-field of magnet in Cartesian coordinates (Bx, By, Bz) in units of mT/(kA/m).

Return type:

ndarray, shape (n,3)

Examples

Compute the field of two different spherical magnets at position (1,1,1), inside and outside.

>>> import numpy as np
>>> import magpylib as magpy
>>> dia = np.array([1,5])
>>> obs = np.array([(1,1,1), (1,1,1)])
>>> mag = np.array([(1,2,3), (0,0,3)])
>>> B = magpy.core.magnet_sphere_field('B', obs, mag, dia)
>>> print(B)
[[0.04009377 0.03207501 0.02405626]
 [0.         0.         2.        ]]

Notes

The field corresponds to a dipole field on the outside and is 2/3*mag in the inside (see e.g. “Theoretical Physics, Bertelmann”).

magpylib.core.magnet_tetrahedron_field(field: str, observers: ndarray, magnetization: ndarray, vertices: ndarray) → ndarray#

Magnetic field generated by a homogeneously magnetized tetrahedron.

Parameters:

field (str, default=`'B'`) – If field=’B’ return B-field in units of mT, if field=’H’ return H-field in units of kA/m.
observers (ndarray, shape (n,3)) – Observer positions (x,y,z) in Cartesian coordinates in units of mm.
magnetization (ndarray, shape (n,3)) – Homogeneous magnetization vector in units of mT.
vertices (ndarray, shape (n,4,3)) – Vertices of the individual tetrahedrons [(pos1a, pos1b, pos1c, pos1d), (pos2a, pos2b, pos2c, pos2d), …].

Returns:

B-field or H-field – B/H-field of magnet in Cartesian coordinates (Bx, By, Bz) in units of mT/(kA/m).

Return type:

ndarray, shape (n,3)

Examples

Compute the B-field of two different tetrahedron-observer instances

>>> import numpy as np
>>> import magpylib as magpy
>>>
>>> obs = np.array([(1,2,3), (2,3,4)])
>>> mag = np.array([(222,333,444), (111,112,113)])
>>> vert = np.array([((-1,0,0), (1,-1,0), (1,1,0), (0,0,1))]*2)
>>> B = magpy.core.magnet_tetrahedron_field('B', obs, mag, vert)
>>> print(B)
[[0.19075398 0.8240532  1.18170862]
 [0.03125701 0.08445416 0.1178967 ]]

Notes

The tetrahedron is built up via 4 faces applying the Triangle class, making sure that all normal vectors point outwards, and providing inside-outside evaluation to distinguish between B- and H-field.

magpylib.core.triangle_field(field: str, observers: ndarray, magnetization: ndarray, vertices: ndarray) → ndarray#

Magnetic field generated by homogeneous (magnetic) charges on triangular surfaces.

Can be used to compute the field of a homogeneously magnetized bodies with triangular surface mesh. In this case each Triangle must be defined so that the normal vector points outwards.

Parameters:

field (str, default=`'B'`) – If field=’B’ return B-field in units of mT, if field=’H’ return H-field in units of kA/m.
observers (ndarray, shape (n,3)) – Observer positions (x,y,z) in Cartesian coordinates in units of mm.
magnetization (ndarray, shape (n,3)) – Homogeneous magnetization vector in units of mT. The triangle surface charge is the projection of the magnetization vector onto the surface normal vector. The order of the vertices defines the sign of the normal vector (right-hand-rule).
vertices (ndarray, shape (n,3,3)) – Vertices of triangular faces of the format [(pos1a, pos1b, pos1c), (pos2a, pos2b, pos2c), …]. The vertex order defines the normal vector orientation of the face (right-hand-rule).

Returns:

B-field or H-field – B/H-field of magnet in Cartesian coordinates (Bx, By, Bz) in units of mT/(kA/m).

Return type:

ndarray, shape (n,3)

Examples

Compute the B-field of two different triangle-observer instances.

>>> import numpy as np
>>> import magpylib as magpy

>>> mag = np.array([(22,33,44), (33,44,55)])
>>> vert = np.array([((-1,0,0), (1,-1,0), (1,1,0))]*2)
>>> obs = np.array([(1,2,3), (2,3,4)])
>>> B = magpy.core.triangle_field('B', obs, mag, vert)
>>> print(B)
[[0.08836711 0.27062047 0.42198603]
 [0.09721743 0.17609525 0.23937461]]

Notes

Field computations implemented from Guptasarma, Geophysics, 1999, 64:1, 70-74. Corners give (nan, nan, nan). Edges and in-plane perp components are set to 0. Loss of precision when approaching a triangle as (x-edge)**2 :( Loss of precision with distance from the triangle as distance**3 :(

magpylib.core package

Contents

magpylib.core package#