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Statement of a problem № 132

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In a certain two-dimensional field of force the potential energy of a particle has the form U = ax^2+by^2, where a and b are positive constants whose magnitudes are different. Find out: (a) whether this field is central; (b) what is the shape of the equipotential surfaces and also of the surfaces for which the magnitude of the vector of force F = const.

Solution:
In a certain two-dimensional field of force the potential energy of a particle h

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