The constant, K, in Coulomb’s equation is much larger than the constant, G, in the universal gravitation equation. Of what significance is this?

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ncchemist | eNotes Employee

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Gravitational and electrostatic forces are part of a group of forces in physics that are called fundamental forces.  Coulomb's law and the law of universal gravitation are both examples of inverse square laws, meaning that the force between two objects is inversely proportional to the square of the distance between the two objects.

Coulomb's law is shown below:

F = K*(q1*q2)/r^2

where F is the electrostatic force, K is Coulomb's constant, q1 and q2 are the scalar charges of the two objects, and r is the distance between the two objects.  The value of K is 8.987 x 10^9 N*m^2/C^2.

The law of universal gravitation is shown below:

F = G*(m1*m2)/r^2

where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the two objects.  The value of G is 6.67 x 10^-11 N*m^2/kg^2

Basically, the reason that Coulomb's constant is so much larger than the gravitational constant is that gravitational force is much weaker than other fundamental forces, including electrostatic force.  Here is a real life example to demonstrate the point.  If you take a balloon, rub it on your shirt, and then place it on a wall, the static electrostatic force will cause the balloon to stick to the wall.  The electrostatic force is plainly evident.  But if you did not rub the balloon and placed it near the wall, there would be no obvious force or attraction between the wall and the balloon.  In other words, the gravitational force of attraction between the balloon and the wall is present, but it is so small that it essentially rounds down to zero.  In fact, the force of the static electricity overcomes the force of gravity between the balloon and the Earth (the balloon sticks to the wall instead of falling to the floor).  You have to get objects on the size of planetary scales to get appreciable gravitational forces.