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Lecture 4 Electric Potential Conductors Dielectrics. Electromagnetics Prof. Viviana Vladutescu. Electric Potential. Electric Potential. The electric field intensity is acting as a force on any charges it arrives upon.

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lecture 4 electric potential conductors dielectrics

Lecture 4Electric PotentialConductors Dielectrics


Prof. Viviana Vladutescu

electric potential
Electric Potential

The electric field intensity is acting as a force on any charges it arrives upon.

Therefore in moving a unit charge from P1 to P2, work must be done against the field.


When force is applied to move an object, work is the product of the force and the distance the object travels in the direction of the force





Thereforewithout specifying the path

The scalar line integral of an Irrotational (conservative) E field is path-independent

equipotential surfaces
Equipotential surfaces

A set of points with same potential forms equipotential surface. For a point charge, equipotentials are spheres

at fixed radius r.

Consider the plot of the electrostatic potential contours forming equipotential surfaces around the point charge superimposed over the field lines for the point charge


As we can notice the field goes into the direction of decreasing potential

If the behavior of the potential is unknown, the electric intensity field can be determined by finding the maximum rate and direction of the spatial change of the potential field


Absolute potential at some finite radius from a point charge fixed at the origin (reference voltage of zero at an infinite radius)

Work per Coulomb required to pull a charge from infinity to the radius R


If the electrical force moves a charge a certain distance, it does work on that charge. The change in electric potential over this distance is defined through the work done by this force: Work done=Charge on Q*Potential

where potential is shorthand for change in electric potential, or potential difference. This is analogous to the definition of the gravitational potential energy through the work done by the force of gravity in moving a mass through a certain distance. The units of potential difference, or simply potential, are Joules / Coulomb, which are called Volts (V). Physically, potential difference has to do with how much work the electric field does in moving a charge from one place to another.

Batteries, for example, are rated by the potential difference across their terminals. In a nine volt battery the potential difference between the positive and negative terminals is precisely nine volts. On the other hand the potential difference across the power outlet in the wall of your home is 110 volts.

Are caractherized by ε, μ and σ

The conductivity σ (S/m or 1/Ω*m or mhos/m)

-depends on the charge density ρ

-depends on the temperature

Ex of superconductors: yttrium-barium-copper-oxide

current and current density
Current and Current Density
  • Current
  • Current



Types of current

-conduction currents: present in conductors and semiconductors and caused by drift motion of conduction e- or holes in a media in response to an applied field ex:

J=σ* E (conduction current density)

-displacement or electrolytic currents: is the result of migration of positive and negative ions as well known as time-varying field phenomenon that allows current to flow between plates of a capacitor.

-convection currents: involve the movement of charged particles through vacuum, air or other nonconductive media (e- in a cathode ray tube)



J & E


of charge

conduction currents
Conduction currents

For most conducting materials the average drift velocity is directly proportional to el field intensity

conductors in static electric field
Conductors in static electric field

Under static conditions the E field on a conductor surface is everywhere normal to the surface (the surface of a conductor is an equipotential surface under static conditions)


-The tangential component of the E field on a conductor surface is zero -The normal component of the E field at a conductor /free space boundary is equal to the surface charge density on the conductor divided by the permittivity of free space

Charactheristics of E on conductor

/free space interfaces


-Ideal dielectrics do not contain free charges

-contain bound chargesInduced electric dipoles

The material is polarized

Polar molecules (Permanent dipole moment)

Nonpolar molecules

Ex: By aligning the molecules during the fabrication of a material (use E field when the material is melted and maintain it until it solidifies) we can obtain electrets

the volume density of the electric dipole moment
The volume density of the electric dipole moment

Vector sum of the induced

dipole moments

Polarization vector

n-#of molecules per unit volume

polarization charge densities
Polarization charge densities



A polarized dielectric may be replaced by an equivalent polarization surface charge density and an equivalent polarization volume charge density for field calculation