7: Summary
 Electric interactions involve electric charge, measured in units of Coulombs.
 The electric field \(\mathbf{E}\) is a vector field. It contains all of the information required to determine the force on a charge \(q\) placed in the electric field, using \[\mathbf{F} = q \mathbf{E}\]. Units of the electric field are Newtons per Coulomb (N/C), or equivalently Volts per meter (V/m).

By convention, electric fields point away from positive charges and toward negative charges. Field lines may only start or end on charges. If they do not end, they either loop around on themselves or extend toward infinity.

The electric potential, \(V\), is a scalar field, having units of Volts. How quickly the electric potential changes along a distance \(r\) indicates the strength of the electric field in that direction. \[\mathbf{E} = \dfrac{\Delta V}{\Delta r}= \dfrac{\mathrm{d}V}{\mathrm{d}r}\]

Both the electric field and the electric potential can be determined entirely from information about the source charges. The principle of superposition allows us to add the effects of multiple charges to find the total \(\mathbf{E}\) and \(V\).

Electrical force is an interaction between two or more charges. For two point charges \(q_1\) and \(q_2\) this force can be calculated directly \[ \mathbf{F}_{q_1 \text{ on } q_2}  =  \mathbf{F}_{q_2 \text{ on } q_1}  = \dfrac{k q_1 q_2}{r^2}\] It can also be determined from the field created by the source charges (using \(\mathbf{F} = q \mathbf{E}\) like above), or determined by how the potential energy changes with distance \[ \mathbf{F}  = \dfrac{\Delta PE}{\Delta x}\]

Concepts in this chapter have several common representations:

A vector map: This representation for the electric field shows individual field vectors at a grid of points.

A field line map: This representation for the electric field uses continuous lines. The actual field is tangent to the field lines at any point. The strength is determined by how close together the field lines are.

Equipotentials: This representation for the electric potential indicates regions (dotted lines usually) where the electric potential takes the same value. Where the potential changes quickly, the electric field is large.