Electrostatic force

In physics, the electrostatic force is the force arising between static (that is, non-moving) electric charges. This force is proportional to the product of the electric charges, and inversely proportional to the distance between the charges. The magnitude of the force takes the form:

<math>F=\frac{1}{4\pi \epsilon _0}\frac{q_1q_2}{r^2}<math>

where F is the magnitude of the force (in newtons),

<math>\epsilon _0<math> is the permittivity of free space,

<math>q_1<math> and <math>q_2<math> are the charge magnitudes (in coulombs),

and r is the distance between the two charges in metres. The direction of the force vector is along the axis joining the two charges, which can be expressed in the following vector equation:

<math>\mathbf{F}=\frac{1}{4\pi \epsilon _0}\frac{q_1q_2\mathbf{r}}{r^3}<math>

where <math>\mathbf{F}<math> is the electrostatic force vector,

and <math>\mathbf{r}<math> is the vector between the two charges, such that

<math>\mathbf{r}=\mathbf{r_1}-\mathbf{r_2}<math>

where <math>r_1<math> is the charge on which the force acts,

and <math>r_2<math> is the other charge. Note that when <math>q_1<math> and <math>q_2<math> are the same sign the force vector acts in the same direction as r – Like charges repel. When they are of opposite signs the force vector acts in the opposite direction to r – unlike charges attract.

In the cgs system of measurement, the force coefficient is included in the unit definitions, giving the simpler equation:

<math>\mathbf{F}=\frac{q_1q_2\mathbf{r}}{r^3}<math>

where <math>\mathbf{F}<math> is the force vector (in dynes),

<math>q_1<math> and <math>q_2<math> are the charges (in statcoulombs),

and <math>\mathbf{r}<math> and <math>r<math> are the distance vector and magnitude, measured in centimetres. The above equation can also be interpreted in terms of atomic units with the force expressed in Hartrees per Bohr radius, the charge in terms of the elementary charge, and the distances in terms of the Bohr radius.