RegisterDuality principleInvestigating Maxwell equations |
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we can simply understand, that exchanges transform the left-hand side of equations to right-hand side and vice versa. Performing similar exchanges, the solution of right-hand set of equations can be obtained from the solution of left-hand side set under the same boundary conditions. E.g., two similar tasks are assumed, which differ by feeding (electric current in the first case, magnetic current in the second one) only. Solution of the first task is based on the left-hand couple of equations (1), (2), solution of the right-hand task on the right-hand couple. Solution of the first task is known, solution of the second task is rather problematic. According to the duality principle, solution of the second task is obtained by exchanging (3) in the result of the first task. Conditions for the application of the duality principle are met at complementary objects. Two complementary objects are two planar objects. At the first one, a part of the plane is conductive (metal), the rest is not conductive (air). At the second object, the situation is reverse. E.g., a slot is complementary to a conductive strip, both the slot and the strip have to be of identical dimensions. In the strip, electric current can be excited, and the strip radiates as a dipole. In the slot, magnetic current is excited. Relation for slot radiation is the same as relation for dipole radiation if exchanges (3) are done. Back
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