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3.5 The interaction of the two fixed spherical sources and drains

   

Consider a classical mechanical Faraday-Maxwell posing the problem of interaction between two spherical objects, emitting or absorbing streams ether particles.

Following Maxwell terms, objects emitting material particles will be called sources and absorbing - drains. According to the concepts of the Faraday ether is some incompressible liquid medium filling the space. Applying the principle of superposition of velocity fields, well-known circuits receive mechanical interaction models sources and drains (Fig. 3.5.1, 3.5.2).

Current lines indicated by dashed lines, define the path of movement of particles of ether flows.

source drain

Fig. 3.5.1

source source

Fig. 3.5.2

Configuration particles arrangement streamlines in the case of interaction with the drain stream will be similar to the configuration of the current source of interaction with the source lines (Fig. 3.5.2). The difference will be only that the line current in this case will be sent to the drains.

Consider two material objects: I - source and II - drain and limited surface of the sphere radii  and , (Fig. 3.5.3). We distinguish on the field object surface element I (Ring) enclosed between the sections formed by two coaxial cones forming an angle . The tops of the cones are in the center of a sphere of radius  And the direction of the axes coincides with a unit vector .

object I (source) object II (drain)

















Fig. 3.5.3

Where:  – distance between centers of objects I and II;

- the unit vector direction of the object I center to center of object II; 
– the unit vector normal to the outer surface of the element ;

 – the angle between the unit vector  and the unit vector;

– angle increment ;

- the angle between the segment joining surface with the center of the object II and the direction of the unit vector ;

- vector ether stream rate emitted by the object I surface c ;

- density ether particles filling the space; 

– vector ether stream rate absorbed from the surface of the object II ;

- acceleration vector ether flux emitted from the surface of the object I ;

- acceleration vector stream ether absorbed from the surface of the object II ;

- ether product of the density of particles on the modulus of the sum stream velocities in the projection onto the unit vector ;

- total acceleration vector particles flows;

- an element of the object I surface;

or, passing to the limit: . (3.5.1)

Applying the principle of superposition of velocity fields and particle accelerations ether define expression for the projection of the force acting on the spring in the direction I , By reacting the drain II (see section 3.3):

(3.5.2)

Performing the calculations, and substituting in equation (3.5.2) value ds of the equation (3.5.1), we obtain:

(3.5.3)

For sufficiently large distances between the interacting objects when  and the angle  tends to zero, and  - unit and the distance from the object II to the center element surface tends to , We obtain:

(3.5.4)

Substituting in equation (3.5.4) of the previously obtained values ​​of the equations (3.3.5) - (3.3.8) define the expression for the projection of the force acting on the spring in the direction I by reacting with a drain II:

source I – drain II

=

(3.5.5)

Similarly, we obtain the expression for the force acting on the object I in the following cases:

source I - source II

(3.5.6)

drain I - source II

(3.5.7)

drain I - drain II

(3.5.8)

Taking the assumption that the intensity of the source proportional to the mass of the source , And the intensity of runoff  proportional to the mass stream , We obtain:

(3.5.9)

(3.5.10)

Where: и – proportionality coefficients intensity of the source and drain, respectively;

and - density substance source and drain, respectively.

Replacing one of the factors  and in the second term of (3.5.5) - (3.5.8) on its value from equations (3.5.9), (3.5.10), and by changing the places of the terms, we obtain:

source I – drain II

(3.5.11)

source I – source II

  (3.5.12)

drain I – source II

(3.5.13)

drain I – drain II

(3.5.14)

Equating to zero the equation (3.5.11) - (3.5.14), we define the value of , In which the graph of the function intersects the axis . In Fig. 3.5.4 and 3.5.5 are graphs of the forces acting on the object I, depending on the distances between the objects. As shown in the graphs, the intersection with the axis It will occur only for interactions source - drain and drain - source. More accurate charting at close distances get further in the study of the function of the equation (3.5.3), characteristic for the weak and nuclear interactions.

                                                                                                             

                                                                                

 

Fig. 3.5.4  Fig. 3.5.5

The present study allows to establish a hitherto unknown interaction forces dependent objects from the speed and acceleration ether streams emitted and absorbed sources and drains.