A general approach to the problem of optimization of magnetic systems of permanent magnets is formulated. The potential of the method is illustrated using the example of Systems producing a maximum magnetic field in a given point of space. For two types of geometry, a solution is: obtained that gives an optimum distribution of magnetization and an optimum shape of the region occupied by a magnetically hard material. The possibility of creating, in a local region of space, a magnetic field several times as great as the residual induction of the material of the magnet is shown.
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