As far as physicists know there are only four fundamental forces in nature. These are: two kinds of nuclear forces, the force of gravity and the force of electricity and magnetism. We consider the force of electricity and magnetism (E&M) together, because they turn out to be only different faces of the same force, depending on the motions considered. But we will not be concerned with that aspect here, nor will we discuss the nuclear forces. Of the two E&M faces we will examine only the electrical force, or to be more exact, the electrostatic force. What we are especially concerned with here is comparing this force with gravity for some specific cases to make some important points. One such point is that the electrical force is so strong that only a few charges can produce forces greater than those of gravity due to large masses, and we will give some examples. We are usually more aware of gravity in everyday life because the charges in our experiences are often cancelled out by other charges of a different sign, and it is only the net charge, after this cancellation, that is important (as in Equations 1, 2, and 3 below), and by contrast, gravity-masses cannot cancel out. There is only one kind of gravity-mass. We find few big exceptions (e.g., electrical power plants) to the fact that we are usually more aware of gravity, and how often do we visit these enterprises? Now we try to give some idea of the importance of what happens when electrical charges don't balance and compare the resulting electrostatic force to a fair measure of the gravity force.

The Equations

        Force of gravity = F_g =GM₁M₂/R²,                                  (1)

where G is the universal gravitational constant, M₁ and M₂ are the masses of objects 1 and 2, respectively, and R is the distance between the two objects.

        Electrostatic force = F_E = (1/4pe₀)Q₁Q₂/R²,                      (2)

where e₀ is the permittivity of free space and Q₁ and Q₂ are the net charges on objects 1 and 2, respectively. R again is the distance between the two objects. By "net" charges we mean what remains after plus and minus charge cancellation. [For example, if Q₁ is made up of 7 plus and 3 minus charges, it is worth only 4 (=7-3) charges. Similarly for Q₂.]

        We find it convenient to take a ratio of these two forces, because we want to compare them (and for another reason that will become apparent):

        F_E/F_g = (1/4pGe₀)Q₁Q₂/M₁M₂ = K x (Q₁/M₁) x (Q₂/M₂),     (3)

where K = 1/4pGe₀ and Q₁/M₁ and Q₂/M₂ are ratios of the charge to mass of an object. Notice that the ratio F_E/F_G contains all of the quantities that F_E and F_G did individually, except for the distance between the objects, R, which has been "cancelled away." In other words, once we know K (= 1/4pGe₀) and given the charge to mass ratios, Q₁/M₁ and Q₂/M₂, the ratio of forces, F_E/F_g, will be the same for two objects that are one inch apart or a million miles apart. Click here for more on equation 3. Click here for more information and challenge material on this subject.

Although for those less familiar with this area of physics or science these equations and calculations may appear intimidating, together they illustrate a simple fact: nature has miraculously conspired to balance positive and negative electrical charges to an astounding degree of accuracy, so that gravity deceptively appears to us in our everday lives to be the stronger force. As illustrated by the first row of the table, if we increased the number of electrons in two people standing two meters apart by just 1/100 of 1% without increasing by a like amount their positive charge, the electrostatic force would overwhelm gravity, making human presence on Earth impossible. The second line shows that by putting the boy's charge out of balance by only 1/10,000,000 and adding the same out-of-balance charge at the far distance of the Earth's center, the force on the boy becomes 30 times the force of gravity. If we did this quickly, he would take off like a rocket. There are such out-of-balance charges (i.e., lightning discharges), and greater, at various parts of the Earth from time to time, but the boy is always in perfect charge balance, so he still experiences only the force of gravity. These demonstrate but two examples of the finely tuned and fragile balance so prevalent in nature and hopefully will instill in the reader some appreciation of the awe so often experienced by physicists studying nature's subtle balances.