Electric energy and potential

Potential energy

An object near the surface of the Earth has a potential energy because of its gravitational interaction with the Earth; potential energy is really not associated with a single object, it comes from an interaction between objects.

Similarly, there is an electric potential energy associated with interacting charges. For each pair of interacting charges, the potential energy is given by:

electric potential energy: PE = k q Q / r

Energy is a scalar, not a vector. To find the total electric potential energy associated with a set of charges, simply add up the energy (which may be positive or negative) associated with each pair of charges.

An object near the surface of the Earth experiences a nearly uniform gravitational field with a magnitude of g; its gravitational potential energy is mgh. A charge in a uniform electric field E has an electric potential energy which is given by qEd, where d is the distance moved along (or opposite to) the direction of the field. If the charge moves in the same direction as the force it experiences, it is losing potential energy; if it moves opposite to the direction of the force, it is gaining potential energy.

The relationship between work, kinetic energy, and potential energy:

Electric potential

Electric potential is more commonly known as voltage. The potential at a point a distance r from a charge Q is given by:

V = k Q / r

We define V=0 when r=infinity.
Potential plays the same role for charge that pressure does for fluids. If there is a pressure difference between two ends of a pipe filled with fluid, the fluid will flow from the high pressure end towards the lower pressure end. Charges respond to differences in potential in a similar way. Electric field lines point towards regions of lower potential.

Electric potential is a measure of the potential energy per unit charge. If you know the potential at a point, and you then place a charge at that point, the potential energy associated with that charge in that potential is simply the charge multiplied by the potential. Electric potential, like potential energy, is a scalar, not a vector.

connection between potential and potential energy: V = PE / q

To find the total electric potential associated with a set of charges, simply add up the potential due to the individual charges (which may be positive or negative).

If we know the electric field (say from gauss' law) then we can determine the potential by using equantion 23-3 from Giancoli.

Equipotential lines

Equipotential lines are connected lines of the same potential. These often appear on field line diagrams. Equipotential lines are always perpendicular to field lines, and therefore perpendicular to the force experienced by a charge in the field. If a charge moves along an equipotential line, no work is done; if a charge moves between equipotential lines, work is done.

Field lines and equipotential lines for a point charge, and for a constant field between two charged plates, are shown below: