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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Prof. Viviana Vladutescu
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
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.
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
-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
For most conducting materials the average drift velocity is directly proportional to el field intensity
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
-contain bound chargesInduced electric dipoles
The material is polarized
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
Vector sum of the induced
n-#of molecules per unit volume
D = εE
A polarized dielectric may be replaced by an equivalent polarization surface charge density and an equivalent polarization volume charge density for field calculation