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DIELECTRIC EFFECTS FROM DIVERGENT ELECTRIC FIELDS:
Most textbooks in physics describe how a piece of paper or a neutral dielectric object can be picked up with a charged glass rod. This is the divergent electrical field at work. It polarizes and generates a net attraction on the dielectric object. A dielectric object is always drawn away from a region of a weak field towards a region of a strong field, as seen in figure 6. The polarity of the field does not affect the direction of the force. 





Figure 6. A nonuniform electrical field will generate a net attractive force on a neutral piece of matter. The force is directed toward the region of higher field strength.
The net force on the dielectric is proportional to the gradient of the square of the field times the volume of the dielectric (P. Lorrain and D. Corson) , given by : 





We can calculate the divergent Em field from a hydrogen atom due to the motion of the electron charge. Knowing the magnitude and divergence of the Em field, we can find the force that pulls on a nearby atom, in accordance with Eq. (5.0).
In view of quantum mechanics, the Bohr model is an oversimplification. However, as we will see, this approach offers some insights into the nature and magnitude of the force generated by the divergent motional electric field. It is very much like Feynman's calculation of the atomic magnetic moment using classical mechanics (Feynman) that turns out to be quite accurate 





It is worth noting that the electron spin itself does also generate a motional electric field. This effect will be ignored in our discussion since it can be shown that it falls off faster than the motional electric field produced by the circulating electron. It may be speculated that the motional electric fields generated by spinning elementary particles has some relationship to nuclear forces, but this is not discussed here.
Since a hydrogen atom can be considered a tiny dielectric, it is attracted towards the source of a diverging E m field. We can calculate the instantaneous force generated by the diverging E m field from Eq. (5.0). The instantaneous force for various positions of the moving electron is plotted in figure 9. Assuming that the ycomponents will cancel we can find the sum of the xcomponents. When measured at point P, the sum of all the xvectors will not completely cancel, due to a small difference in magnitude between distance R+x and Rx.
Mathematically, the dielectric force produced by a single atom acting on another dielectric atom can be found by integrating one revolution of the moving electron (ignoring the y and z components, for now) by using Eq. (5.0): 


 
