Coulomb’s law question

Question

Compare and contrast Coulomb’s law to universal gravitation by explicitly stating the likeness and differences of the two rules.

Answer 1

Let's start by defining the equations and variables:

Coulomb's Law: F = k* (q1*q2)/r^2

F = Coulombic Force [N]

q1, q2 = electric charges [C]

k = Coulomb's constant = 8.988*10^9 [N*m^2/C^2]

r = distance of separation [m]

Universal Gravitation: F = G*(m1*m2)/r^2

F = Gravitational Force [N]

m1,m2 = masses [kg]

G = Gravitational constant = 6.6743*10^-11 [N*m^2/kg^2]

r = distance of separation [m]

Some Similarities:

1. Both equations look very similar because they are describing the same relationship between two bodies, caused by two different things. Both equations describe the attraction ( or repulsion) of two bodies due to a parameter of the body.
2. Both relationships are inversely proportionate to the distance of separation ( both have r^2 in the denominator.
3. The range of both of these forces are technically infinite, meaning that any two bodies that have mass or an electric charge anywhere in the universe are exerting a force on one another. (Pretty crazy to think about)

Difference:

1. The gravitational force can only be a force of attraction between two bodies while the Coulombic force can be either attractive or repulsive. Looking at the two equations. the constants are always positive, and the distance of separation must always be positive. Similarly mass is always positive so there is no variable that can make the gravitational force negative. However we know that electric charges can be either positive or negative and as a result the Columbic force can be positive or negative. This is seen in real life with opposite charges attracting each other and like charges repelling one another.

Let me know if that helped!