Attachment 261
The potential energy of the gravitational field (not drawn to scale in distance and not weighted in mass function) is shown on the right. The slope is gravity. As the distance increases, the slope approaches zero. As the distance decreases, it approaches infinity. Since gravity is always attractive, the curve never crosses the distance axis.
The electrostatic potential for 2 oppositely charged particles of equal mass (say, an electron and a positron and where their permittivities all have values of unity) can also be described by the same curve. However, for 2 like charges (e.g. electron and another electron) the curve is shown on the left. In this case, the slope is the electric force.
Now, ignoring the effect of magnetic permeability, the magnetic vector potential where the velocity of the charged reference frame is zero, the superposition of these curves (gravity and electric) becomes, when scaled to the distance and weighted mass function, the value of the charge to mass ratio of the test particles.


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