Method of Images in Electrostatics

A three-dimensional field solution is presented foraxially polarized permanent magnet cylinders. The fieldcomponents are expressed in terms of finite sums of elementaryfunctions and are easily programmable. They can be used todetermine the operating point of rare-earth magnet cylinders.They are also useful for performing rapid parametriccalculations of field strength as a function of materialproperties and dimensions. The field components aredeveloped for different magnet arrangements by taking intoaccount the back iron. Also the method of images is used. Usingthe field equations, three-dimensional analytical expressionsare derived for computing the magnetic force between axiallypolarized permanent-magnet cylinders for different magneticarrangements. The field calculated results are in goodagreement with the experimental data.

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Lord Kelvin’s method of images in semigroup theory

Semigroup Forum ◽

10.1007/s00233-010-9230-5 ◽

2010 ◽

Vol 81 (3) ◽

pp. 435-445 ◽

Cited By ~ 11

Author(s):

Adam Bobrowski

Keyword(s):

Semigroup Theory ◽

Method Of Images

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Method of Images*

Handbook of Differential Equations ◽

10.1016/b978-0-12-784391-9.50075-0 ◽

1992 ◽

pp. 279-282

Author(s):

Daniel Zwillinger

Keyword(s):

Method Of Images

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Piecewise Analytic Solutions of Mixed Boundary Value Problems

Canadian Journal of Mathematics ◽

10.4153/cjm-1966-113-6 ◽

1966 ◽

Vol 18 ◽

pp. 1121-1147 ◽

Cited By ~ 1

Author(s):

M. Eisen

Keyword(s):

Differential Equations ◽

Mixed Problem ◽

Mixed Boundary ◽

Separation Of Variables ◽

Analytic Solutions ◽

General Criterion ◽

Method Of Images ◽

Correct Boundary Conditions ◽

Hyperbolic Differential Equations ◽

Boundary Surfaces

In a mixed problem one is required to find a solution of a system of partial differential equations when the values of certain combinations of the derivatives are given on two or more distinct intersecting surfaces. If the differential equations arise from some physical process, the correct boundary conditions are usually apparent. Many particular problems of this type have been solved by special methods such as separation of variables and the method of images. However, no general criterion has been given for what constitutes a correctly set mixed problem. In fact such problems have usually been formulated in connection with hyperbolic differential equations with data prescribed on two surfaces (called the initial and boundary surfaces).

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