Electric Potential

Physics
Vandebilt Catholic High School
W. Dupre

Electric Potential

Two points are said to differ in electric potential if work is done to move a charge from one point to another point in an electric field.

Potential (symbol is V; SI unit is volt (V))

work done on a charge; or the potential energy per unit charge.

Only differences in potential can be measured.

V = W / q or V = DU / q

In a uniform electric field (a parallel plate capacitor):

V = E d DU = qEd

where E is the electric field strength and d is the separation between the plates in meters

Electric Potential Energy

When a charge q moves from point B to point A in an electric field, the change in electric potential energy is simply the negative of the work done to move the same charge from point A to point B. Just as we defined the electric field as the force per unit charge, we will define the electric potential (or potential) as the potential energy per unit charge.

Since only differences in potential are measurable, the potential at point A would simply be the difference in potential energy, or the work done, to move the charge from some point B to point A.

V_BA = V_B - V_A = W_BA/q

Electric potential is a scalar term. When finding the electric potential due to a collection of point charges, you need only add the potentials together with no concern for direction. Include a sign for the potential corresponding to the sign of the charge.

Potential of a Point Charge

The electric potential at a distance d from a single point charge can be derived from the expression for electric field due to a point charge. Also called electric potential of a point charge. The expression is:

V = k q / d

Electrostatic energy (U) for point charges can be found. It is simply the same thing as "work" in the definition of voltage. Since the electric potential is defined as the potential energy per unit charge, then the change in potential energy of charge q moved between points a and b is simply equal to qV_ab. In other words,

U = q V
If dealing with point charges, U = qV becomes U = k (q₁q₂)/d. If one is trying to find the total electrostatic energy due to a system of charges, one finds the sum of the electrostatic energies between each charge. As in absolute potential, one includes the sign of the charge.

Relationship Between Electric Potential and Electric Field One can describe the effects of charge distribution using either electric field or electric potential. Electric potential can be easier to use than electric fields because it is a scalar quantity rather than a vector quantity.

In a uniform field (such as between two parallel plates), the units for electric field (N/C) can be written as V/m. We find that E = V/d in a uniform field.

Remember field lines point toward the negative plate. By convention the negative plate is said to be at a lower potential than the positive plate. Therefore a point closer to the positive plate is said to be at a higher potential than a point closer to the negative plate (nearer the arrow of the field line).

Equipotential Lines Just as electric field lines represented the electric field around a charge, equipotential lines represent the electric potential about a charge. In three dimensions, they become equipotential surfaces.

Equipotential Surface An equipotential surface is one on which all points are at the same potential. The potential difference between any two points on an equipotential surface is zero; there is no work done to move a charge between these two points.

Characteristics of Equipotential Surfaces

No work is done to move a charge between two points on the same equipotential surface.

Electric field lines are perpendicular to equipotential surfaces.

The surface of a conductor is an equipotential surface. (A conductor must be entirely at the same potential. There is no electric field within a conductor because otherwise an electron would experience a force and would move.)

Electron Volt (eV)A unit used to deal with the energy of electrons. One electron volt is defined as the energy acquired by an particle carrying a charge equal to that of the electron as a result of moving through a potential difference of 1 V. It is not an SI unit, just an easier unit to use than Joules sometimes.

1 eV = 1.6 x 10^-19 J

Capacitors

Capacitor

a device (sometimes called a condenser) that stores charge in the electric field between its plates. Each plate carries the same amount of charge, one plate being negative and the other being positive. A potential difference exists between the two plates.

Capacitance

symbol is C and SI unit is the Farad, F

q = C V

where q is the charge in Coulombs, C is the capacitance, and V is the potential difference.

Capacitance for a parallel-plate capacitor Capacitance is a proportionality constant. It is a constant for a given capacitor. It does not depend upon charge or voltage. Its value only depends upon the structure and dimensions (size) of the capacitor itself. For a parallel-plate capacitor with plates of area A separated by a distance d of air, the capacitance is given by:

C = A / 4pkd

This relationship makes sense. Plates with a larger area will have less repulsion between charges (they're further apart) for a given amount of charge q. Thus, more charge can be held. A greater separation means that the charge on each plate exerts less attractive force on the other plate. Less charge is drawn from the battery, and the capacitance is less.

Dielectric An insulating sheet found in most capacitors between the plates. A dielectric allows higher voltages to be applied without charge crossing the gap. A dielectric allows the plates to be placed closer together without touching, allowing an increased capacitance.

It requires energy to place charges on the plates of a capacitor. When the capacitor is discharged, this electrical energy is released. The energy stored in a capacitor is equal to the work done to charge it.

Energy = ½ C V² = 1/2 q V

where C is the capacitance, q is the charge, and V is the voltage