Engineering Electrodynamics

8 Forces in Electrodynamic Systems

8.1 Principles of Calculation of Forces Acting on Buses and Windings of Transformers

The force dF of the magnetic field of flux density B, acting on an element dl of a conductor carrying the current I, according to Ampere’s law, is expressed by the vector product

$d F = I (d l \times B) = n I d l \cdot B \sin (d l, B) (8.1)$

The electromagnetic force acting on a body of volume V, in which flows the electric current of density J = σE, is expressed by Ampere’s law

$\begin{matrix} F = \int_{V} (J \times B) d V & or & d F = (J \times B) d V \end{matrix} (8.2)$

where for an alternating field, E_m = E_m e^jω t, B_m = B_m e^jω t, the force components are

$\begin{matrix} \begin{array}{l} F_{x} = 1 / 2 σ Re (E_{m y} B_{m z}^{*} - E_{m z} B_{m y}^{*}) \\ F_{y} = 1 / 2 σ Re (E_{m z} B_{m x}^{*} - E_{m x} B_{m z}^{*}) \\ F_{z} = 1 / 2 σ Re (E_{m x} B_{m y}^{*} - E_{m y} B_{m x}^{*}) \end{array} & } \end{matrix} (8.2a)$

The most popular, four basic methods of calculating electrodynamic ...

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Engineering Electrodynamics by Janusz Turowski, Marek Turowski

8 Forces in Electrodynamic Systems

8.1 Principles of Calculation of Forces Acting on Buses and Windings of Transformers

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