Coulomb's Law

To quantify electric interactions we use an equation known as Coulomb's Law $$\vec{F}_{elec\space on \space 2 \space by \space 1} = \frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{|\vec{r}|^2}\hat{r}$$
$\vec{r} = \vec{r}_2 - \vec{r}_1$ is the position of 2 relative to 1.
$\frac{1}{4\pi\epsilon_0}$ is a universal constant, equivalent to $9\times10^9 \frac{Nm^2}{C^2}$
The charges $q_1$ and $q_2$ are measured in units of Coulombs, abbreviated $C$.

Like gravity, it is proportional to the inverse square of the distance between the center of its objects.  The universal constant is much larger than that of the gravitational constant, meaning that the electric interaction is much stronger than gravitational interaction.

Gravitational Force

The gravitational force is between at least two objects.  It:

• Acts along a line connecting the two objects.
• Is proportional to the masses.
• Is inversely proportional to the square of the distance between the centers of the two objects.

It can be modeled in several different ways.  The approximate gravitational force is $$|\vec{F}_{grav}| = mg$$However, there is a much more accurate, albeit complicated, way of determining the forces of gravity.  To determine the force of gravity from one object upon another, you simply use the equation:$$\vec{F}_{grav \space on \space 2 \space by \space 1} = -G\frac{m_1 m_2}{|\vec{r}|^2} \hat{r}$$
$\vec{r} = \vec{r}_2 - \vec{r}_1$ extends from the center of object 1 to object 2.
$G = 6.7 \times 10^-11 \frac{N m^2}{kg^2}$ and is known as the gravitational constant ($G$).

To calculate the magnitude of gravitational field near an object's surface, use the equation:$$g = G\frac{M_E}{R_E^2}$$