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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 l.jpg

Lecture 4Electric PotentialConductors Dielectrics

Electromagnetics

Prof. Viviana Vladutescu



Electric potential l.jpg
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.


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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


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P of the force and the distance the object travels in the direction of the force1

E

P2

Thereforewithout specifying the path

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


Equipotential surfaces l.jpg
Equipotential surfaces of the force and the distance the object travels in the direction of the force

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


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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



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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


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For a collection of charges of continuous distribution fixed at the origin (reference voltage of zero at an infinite radius)


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Review fixed at the origin (reference voltage of zero at an infinite radius)

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.


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  • 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.


Conductors l.jpg
Conductors 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.


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Are caractherized by 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.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 l.jpg
Current and Current Density 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.

  • Current

  • Current

    density


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Types of current 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.

-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)


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V=I*R 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.

J & E

Conservation

of charge


Conduction currents l.jpg
Conduction currents 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.

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


Conductors in static electric field l.jpg
Conductors in static electric field 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.

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)


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-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


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Dielectrics surface is zero


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-Ideal dielectrics do not contain free charges surface is zero

-contain bound chargesInduced electric dipoles

The material is polarized


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Polar molecules (Permanent dipole moment) surface is zero

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


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The volume density of the electric dipole moment surface is zero

Vector sum of the induced

dipole moments

Polarization vector

n-#of molecules per unit volume


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Homogeneous & linear & isotropic media surface is zero

D = εE

D=ε0E+P


Polarization charge densities l.jpg
Polarization charge densities surface is zero

-surface

-volume

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


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Total Charge surface is zero


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