Magnetic flux

Magnetic flux

Magnetic flux is the flux of the magnetic induction vector through any surface. It is defined as

Magnetic flux

where is the vector corresponding to the elementary area ds of the surface S and directed normally with respect to it (Fig. 1.3, a) ds If the magnetic induction is normal to the surface ds, then

those. magnetic induction is the magnetic flux density at a given point in the field.

Magnetic flux

Magnetic flux is measured in weber [Wb] = [V⋅s]. Magnetic induction can be graphically represented by lines whose tangents in each point coincide with the direction of induction, and the number of lines per projector is equal to the numerical value of induction (Fig. 1.3, b). Then the magnetic flux through any surface will be equal to the number of lines passing through this surface. The lines of magnetic field induction are m per unit surface located normally to k in B continuous lines, Fig. 1.3 closed to themselves and having no beginning or end.

Mathematically, the principle of continuity of magnetic lines is formulated as follows:

those. magnetic flux passing through any closed surface is zero. The concept of magnetic flux can be applied to any arbitrarily complex surface, for example, to the surface formed by the turns of the coil in Fig. 1.3, b. Assuming that each turn is almost closed, then this surface can be simplified in the form of several simple flat surfaces 123, s ss and 4 s bounded by separate turns. Therefore, by counting the number of induction lines passing through these surfaces, it is possible to determine the magnetic fluxes that mesh with each turn, and then the total magnetic flux through the entire surface of the electrical circuit of the coil Ψ:

Let the induction lines in Fig. 1.3, b are single magnetic lines. Then

The quantity Ψ is called flux linkage. It can also be determined by summing the number of couplings of each unit line with the turns of the coil. So the first and second lines in fig. 1.3, b are coupled with two turns (), and the third and fourth with four (12 2 Ψ = Ψ = 34 4Ψ = Ψ =). Hence, taking into account the symmetry of the magnetic field pattern

If a magnetic field is created by several currents or turns that may belong to different electrical circuits, then the magnetic flux coupled to some circuit will be equal to the algebraic sum of the fluxes generated by individual currents.

Reference

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