In figure1 it is represented a transversal section of an electrodynamic speaker. This device, characterised by a circular symmetry, has as component parts:

• a core of ferromagnetic material;
• a permanent magnet on the axial direction (respectively across the axis);
• a moving reel which has whirls,situated in the middle of the air-gap.

The moving reel jointed with the membrane, commands the latter's motion, as to create presure waves and, this way, the sound.

• is the medium radius of the air-gap and, thus, the radius of the moving-reel's whirls;
• is the air-gap;
• is the axial lenght of the air-gap;
• is the axial lenght of the reel;
• is the axial lenght of the permanent magnet.

  The characteristic of the permanent magnet is represented in figure 2.

It will be assumed that the operating point of the permanent magnet is situated in the linear area, which can be approximated with the ecuation .

The force which the moving reel, traversed by the current, exerts upon the membrane is mostly of electrodynamic origin. It is the result of the interaction of the current with the field created by the permanent magnet (and, consequently, with the flux intersected by the reel). There is also a reluctant component of the force, produced by the variation of the inductance of the reel, depending on its position. This component is practically negligible comparing to the one of electrodynamic origin.

1.

Calculate the force of electrodynamic origin exerted upon the reel, in the positive direction of x axis when it is traversed by the i current and remains entirely in the air-gap (the permeability of iron will be considered infinite, the air-gap small and the magnetization of the permanent magnet uniform).

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2.

Calculate the force of reluctant origin exerted upon the moving-reel when it is traversed by the i current, using the relation where L_b is the inductance of the reel. The estimation of this force will be made assuming hat the lenght of the reel is negligible (all the whirls are concentrated in x_bposition) and that the magnet is considered a m₀ permeability medium.

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