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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 Difference The 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 field Relationship 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.
Electric Potential Energy 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 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 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
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 Field The 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
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.