Electric Potential

Electric Potential

It takes work to move a charge against an electric field, since the field is defined as the force experienced by a charge. Remember,

Work = Force x distance = change in energy

In electrostatics,

Moving a charge against electric field Moving a mass against gravity

Electric Potential

Just as with the electric field, it is convenient to define a quantity that is the electric potential energy per unit charge. This is called the electric potential.

Unit of electric potential: the volt, V

Count Alessandro Giuseppe Antonio Anastasio Gerolamo Umberto Volta (1745-1827) known for the invention of the battery in 1800

Electric Potential DifferenceThe potential difference between two places is the work a unit charge has to do to move from one place to the other

Just as the potential energy difference for gravity is the work done to move a mass from one place to another

Electric Potential Difference

As with potential energy, only changes in the electric potential can be defined.

The choice of where V = 0 is arbitrary.

Electric Potential Difference

Potential differences are defined in terms of positive charges, as is the electric field. Therefore, we must account for the difference between positive and negative charges.

Positive charges, when released, accelerate toward regions of lower electric potential.

Negative charges, when released, accelerate toward regions of higher electric potential.

(for gravity, mass always accelerates towards regions of lower gravitational potential, since we have no polarity in gravity)

Electric Potential for a point charge

Electric potential difference near a point charge:

Electric Potential and electric fieldRelationship between field and potential for a point charge:

Electric Potential

Whether the electric potential increases or decreases when towards or away from a point charge depends on the sign of the charge.

Electric potential increases when moving nearer to positive charges or farther from negative charges.

Electric potential decreases when moving farther from positive charges or nearer to negative charges.

The electric potential energy of a system of two charges is the change in electric potential multiplied by the charge.

Put another way, the potential energy of a system is the work required to assemble the system (to bring the charges together from far away)

Electric Potential Energy

Electric Potential

The additional potential energy due to a third charge is the sum of its potential energies relative to the first two. Further charges extend the sum.

This is just a consequence of the superposition principle for electric fields.

Electric Potential

Electric forces are conservative forces, so:

•The path chosen to move a charge from one point to another doesn’t matter, the work is the same

•Moving a charge all around space but returning it to where it started results in no energy change of the system

Equipotential Surfaces

An equipotential surface is one on which the electric potential does not vary

•It takes no work to move a charge along an equipotential surface

•Equipotential surfaces are always perpendicular to electric field lines

Electric field lines Equipotential surfaces

Electric Dipole

Equipotential Surfaces

Equipotentials are always perpendicular to electric field lines.

This enables you to draw one if you know the other.

Equipotential Surfaces

Equipotential surfaces outside a conductor

Equipotential Surfaces

Equipotentials are analogous to contour lines on a topographic map.

Equipotentials and the Electric FieldThe direction of the electric field E is that in which the electric potential decreases the most rapidly.

Its magnitude is given by:

In the topological map analogy, the electric field points in the direction of where the mountain is steepest, i.e. the direction in which a ball would roll if you let it go from rest

Different ways of plotting potentials

Electric Potential

Electron-volts

The electron-volt (eV) is the amount of energy needed to move an electron through a potential difference of one volt.

The electron-volt is a unit of energy, not voltage, but is not an SI standard unit.

It is, however, quite useful when dealing with energies on the atomic scale.