Ratio of Electric to Gravitational
Forces

## Question:

A proton and an electron are separated by a distance d. There are
two forces (electric force, Fe & gravitational force, Fg)
acting on them. Why is the Fe/Fg ratio so large? What does it
show? And why doesn't the value 'd' appear in this
ratio, thus not affecting the results?
## Answer:

The law of universal gravitation says that the force due to
gravitational interaction between tow particles is proportional
to the product of their masses divided by the square of the
distance between them. From electrostatics we know that the force
due to the electric interaction between two charged particles is
proportional to the product of their charges divided by the
square of the distance between them. Since both laws involve the
square of the distance between the particles in the same way, the
ratio of the forces will be independent of distance.
Since the distance drops out, the ratio of forces involves two
quantities. One is the ratio of charge^2/mass^2. The other is the
ratio of the electrostatic constant/gravitational constant. In
devising a system of units we are free to select convenient
quantities of charge and mass. Once that choice is made, the
numerical values of the universal constants are measured in terms
of the selected units by experiment. The significance of the huge
ratio between electric and gravitational forces is that in our
chosen system of units, the unit electric charge is much more
effective at distorting the space around them than is the unit
mass.

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understanding how the universe works. My name is James D. Jones.
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JDJ