Magnetic field inside a long cylindrical deflection coil: A closed‐form solution

1986 ◽  
Vol 59 (6) ◽  
pp. 1807-1810
Author(s):  
Basab B. Dasgupta
Keyword(s):  
Magnetic Field ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution

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.

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.

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.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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