Lecture 4 Electric Potential Conductors Dielectrics

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Lecture 4Electric PotentialConductors
Dielectrics

• Electromagnetics
• Prof. Viviana Vladutescu

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Electric Potential
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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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Therefore
without specifying the path
The scalar line integral of an Irrotational
(conservative) E field is path-independent
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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
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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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By using the above in the following equation
we get
Potential difference
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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
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Review
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 doneCharge on QPotential
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.

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Conductors
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Are caractherized by e, µ and s The conductivity
s (S/m or 1/Om or mhos/m) -depends on
the charge density ? -depends on the
temperature Ex of superconductors
yttrium-barium-copper-oxide
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Current and Current Density

• Current
• Current
• density

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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
Js 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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VIR
J E
Conservation of charge
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Conduction currents
For most conducting materials the average drift
velocity is directly proportional to el field
intensity
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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)
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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
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-Ideal dielectrics do not contain free
charges -contain bound charges Induced
electric dipoles
The material is polarized
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• 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
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The volume density of the electric dipole moment
Vector sum of the induced dipole moments
Polarization vector
n-of molecules per unit volume
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Homogeneous linear isotropic media
D eE
De0EP
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Polarization charge densities
-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