MAGNETIC ANOMALY DUE TO A VERTICAL RIGHT CIRCULAR CYLINDER WITH ARBITRARY POLARIZATION

Geophysics ◽  
1978 ◽  
Vol 43 (1) ◽  
pp. 173-178 ◽  
Author(s):  
Shri Krishna Singh ◽  
Federico J. Sabina
Keyword(s):  
Magnetic Field ◽  
Circular Cylinder ◽  
Closed Form ◽  
Magnetic Anomaly ◽  
Closed Form Solution ◽  
Form Solution ◽  
Arbitrary Polarization ◽  
Shaped Body ◽  
Anomalous Magnetic Field

A closed form solution for the total anomalous magnetic field due to a vertical right circular cylinder with arbitrary polarization is derived under the assumption that the magnetization is uniform. As expected, the computed field is similar to the field due to a “similar” prism‐shaped body.

scholarly journals Comparison of closed-form solutions to experimental magnetic force between two cylindrical magnets

2021 ◽  
pp. 141-146
Author(s):  
Sampart Cheedket ◽  
Chitnarong Sirisathitkul
Keyword(s):  
Magnetic Field ◽  
Closed Form ◽  
Magnetic Force ◽  
Permanent Magnets ◽  
Magnetic Levitation ◽  
Closed Form Solution ◽  
Vertical Tube ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Set Up

The force between permanent magnets implemented in many engineering devices remains an intriguing problem in basic physics. The variation of magnetic force with the distance x between a pair of magnets cannot usually be approximated as x-4 because of the dipole nature and geometry of magnets. In this work, the force between two identical cylindrical magnets is accurately described by a closed-form solution. The analytical model assumes that the magnets are uniformly magnetized along their length. The calculation, based on the magnetic field exerted by one magnet on the other along the direction of their orientation, shows a reduction in the magnetic force with the distance x and a dependence on the size parameters of magnets. To verify the equation, the experiment was set up by placing two cylindrical neodymium iron boron type magnets in a vertical tube. The repulsive force between the identical upper and lower magnets of 2.5 cm in diameter and 7.5 cm in length was measured from the weight on the top of the upper magnet. The resulting separation between the magnets was recorded as x. The forces measured at x=0.004-0.037 m differ from the values calculated using the analytic solution by -0.55 % to -13.60 %. The calculation also gives rise to a practical remnant magnetic field of 1.206 T. When x is much large than the equation of force is approximated as a simple form proportional to 1/x-4. The finding can be directly used in magnetic levitation as well as applied in calculating magnetic fields and forces in other systems incorporating permanent magnets.

The Axially Loaded Circular Cylinder

1962 ◽  
Vol 29 (2) ◽  
pp. 318-320
Author(s):  
H. D. Conway
Keyword(s):  
Exact Solution ◽  
Fourier Transform ◽  
Circular Cylinder ◽  
Closed Form ◽  
Cross Sections ◽  
Closed Form Solution ◽  
Form Solution ◽  
Concentrated Force ◽  
Transform Method ◽  
Fourier Transform Method

Commencing with Kelvin’s closed-form solution to the problem of a concentrated force acting at a given point in an indefinitely extended solid, a Fourier transform method is used to obtain an exact solution for the case when the force acts along the axis of a circular cylinder. Numerical values are obtained for the maximum direct stress on cross sections at various distances from the force. These are then compared with the corresponding stresses from the solution for an infinitely long strip, and in both cases it is observed that the stresses are practically uniform on cross sections greater than a diameter or width from the point of application of the load.

To: “Magnetic Anomaly Due to a Vertical Right Circular Cylinder with Arbitrary Polarization”, by S. K. Singh and F. J. Sabina, GEOPHYSICS, v. 43, p. 173–178 (February, 1978)

Geophysics ◽  
1978 ◽  
Vol 43 (6) ◽  
pp. 1312-1312
Keyword(s):  
Magnetic Field ◽  
Circular Cylinder ◽  
Magnetic Anomaly ◽  
Arbitrary Polarization ◽  
Right Hand ◽  
The Right ◽  
The Magnetic Field

There is an error in the paper “Magnetic Anomaly Due to a Vertical Right Circular Cylinder with Arbitrary Polarization”, by S. K. Singh and F. J. Sabina, Geophysics, v. 43, p. 173–178 (February, 1978). The second term of the right‐hand side of equation (5) should be negative. The equation should read: [Formula: see text]. The plot of the magnetic field in Figures 2–4 is correct.

scholarly journals Triple Diffusive Surface Tension Driven Convection in a Composite Layer in the Presence of Vertical Magnetic Field

2020 ◽  
Vol 9 (3) ◽  
pp. 1727-1734
Keyword(s):  
Magnetic Field ◽  
Surface Tension ◽  
Closed Form ◽  
Fluid Layer ◽  
Composite Layer ◽  
Microgravity Condition ◽  
Closed Form Solution ◽  
Form Solution ◽  
Vertical Magnetic Field ◽  
Composite Layers

The problem of triple diffusive surface tension driven convection is investigated in a composite layer in the presence of vertical magnetic field. A closed form solution is obtained under microgravity condition. The parameters suitable for fluid layer dominant and porous layer dominant composite layers are determined. The parameters appropriate for controlling the convection are determined which are useful to manufacture pure crystals.

scholarly journals Closed-Form Solution of Adiabatic Particle Trajectories in Axis-Symmetric Magnetic Fields

2021 ◽  
Author(s):  
F. Sattin ◽  
D.F. Escande
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Closed Form ◽  
Equations Of Motion ◽  
Functional Relation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Low Energy ◽  
Particle Orbit ◽  
Pass Through

The dynamics of a low-energy charged particle in an axis-symmetric magnetic field is known to be a regular superposition of periodic–although possibly incommensurate–motions. The projection of the particle orbit along the two non-ignorable coordinates (x,y) may be expressed in terms of each other: y=y(x), yet–to our knowledge–such a functional relation has never been directly produced in literature, but only by way of a detour: first, equations of motion are solved, yielding x=x(t),y=y(t), and then one of the two relations is inverted, x(t)→t(x). In this paper we present a closed-form functional relation which allows to express coordinates of the particle’ orbit without the need to pass through the hourly law of motion.

scholarly journals Closed-Form Solution of Adiabatic Particle Trajectories in Axis-Symmetric Magnetic Fields

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1784
Author(s):  
Fabio Sattin ◽  
Dominique Franck Escande
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Closed Form ◽  
Equations Of Motion ◽  
Functional Relation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Low Energy ◽  
Particle Orbit ◽  
Pass Through

The dynamics of a low-energy charged particle in an axis-symmetric magnetic field is known to be a regular superposition of periodic—although possibly incommensurate—motions. The projection of the particle orbit along the two non-ignorable coordinates (x,y) may be expressed in terms of each other: y=y(x), yet—to our knowledge—such a functional relation has never been directly produced in literature, but only by way of a detour: first, equations of motion are solved, yielding x=x(t),y=y(t), and then one of the two relations is inverted, x(t)→t(x). In this paper, we present a closed-form functional relation which allows us to express coordinates of the particle’s orbit without the need to pass through the hourly law of motion.

Extension of the Circle Theorems by Surface Source Distribution

1989 ◽  
Vol 111 (3) ◽  
pp. 243-247 ◽  
Author(s):  
O. Rand
Keyword(s):  
Circular Cylinder ◽  
Closed Form ◽  
Closed Form Solution ◽  
Strength Distribution ◽  
Form Solution ◽  
Source Distribution ◽  
Arbitrary Distribution ◽  
Normal Velocity ◽  
Two Dimensional ◽  
Surface Source

The paper presents a closed-form analytical solution for the source strength distribution along the circumference of a two-dimensional circular cylinder that is required for producing an arbitrary distribution of normal velocity. Being suitable to be used with flows having arbitrary vorticity distribution, the present formulation can be considered as an alternative and extensive form of the circle theorems. Using the conformal transformation technique, the formulation also serves as a closed-form solution of Laplace’s equation in any two-dimensional flow domain that is reducible to the outer or inner region of a circular cylinder having arbitrary prescribed normal velocity over its boundary.

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