The gravitational force is much smaller than the force between equivalent electric charges. It is so much smaller than the electric force that it might be considered to be negligible. However, gravity is a real phenomenon, and this great imbalance presents problems in attempting to solve the gravitation problem utilizing electromagnetic theory. The following puzzle is an illustration of this fact.

The Penny Puzzle:The Lincoln penny was originally pure copper, but other metals were added in later years. In this example, we will use the 1910 version, which was originally pure copper. There are

29 electronsand29 protonsper copper atom. The neutrons are electrically neutral and will not be considered. This penny is mostly all copper, and there are2.8 x 10 ^22 copper atoms. Therefore, there are8.12 x 10^23 electrons(that is almost a trillion-trillion electrons) and the same number of protons in one Lincoln penny. Now consider the hypothetical case where the electrons and protons are each grouped together and separated from each other by a distance of100 meters. The problem is to calculate the Coulomb electric force between the two sets of charges.--------------------------------------------------------------------------------------------

The solution is given below:

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Trying to hide the answer so that it is not seen by mistake.

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O.K., you will find the solution by scrolling down:

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The answer to the puzzle:

The solution is obtained by one of the oldest and most reliable laws of physics, the Coulomb equation:

FC = [Ke x (N) ^2] / D^2Newtonswherein the electric constant is

Ke = 2.3019 x 10^-28m^2/N^2 (note that the unit electric charge constants are within this constant).Our equation now appears as:

FC = [2.3019 x 10^-28 x (8.12 x 10^23)^2] / (100)^2.The result is

:

FC = 1.52 x 10^16 Newtons = 3.42 x 10^15 pounds = 1.71 x 10^12 tons= 1.71 trillion tons!This is a number exceeded in our real life only by the

.National DebtThere is however, another problem that was not considered in this hypothetical situation. The forces required to contain this amount of like charges are even higher. Therefore, some other material would need to be added in order to hold the like charges together in a small space.