Lecture 2 The Electric Field.

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Lecture 2The Electric Field.
Chapter 15.4 ? 15.9
Outline

• The Concept of an Electric Field
• Electric Field Lines
• Electrostatic Equilibrium
• Electric Flux and Gauss Law

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The Electric Field
Both the gravitational and electrostatic force
act through space, involving no contact between
the objects involved.

• In order to describe the interaction process
  under these forces, a concept of a field was
  introduced.

An electric field is said to exist in the region
of space around a charged object. When another
charged object enters this electric field, the
field exerts a force on the second object.
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The Electric Field
Consider a small charge q0 near a larger charge
Q. We define the electric field E at the location
of the small test charge as a ratio of the
electric force F acting on it and the test charge
q0
F E ? ? q0
This is the field produced by the charge Q, not
by the charge q0
The direction of E at a point is the direction of
the electric force that would be exerted on a
small positive test charge placed at that point.
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The Electric Field
Once the electric field is known at some point,
the electric force on any charge q0 placed at
that point is
Q q0 F ke ???
r2
F q0E
Q E ke ?? r2
This is the electric field due to a charge Q.
Units ? N/C. If Q is positive, then the field is
radially outward from it. If Q is negative, then
the field is radially toward it.
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Electric Field Lines
To visualize electric field patterns, one can
draw lines pointing in the direction of the
electric field vector at any point. These lines
are called electric field lines.
The electric field vector is tangent to the
electric field lines at each point. The number of
lines per unit area through a surface
perpendicular to the lines is proportional to the
strength of the electric field in a given
region. No two field lines can cross each other.
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Electrostatic Equilibrium
In conductors, electrons are free to move within
the material.
When no net motion occurs within a conductor, it
is said to be in electrostatic equilibrium.

• Properties of an isolated conductor
• The electric field is zero everywhere inside it.
• Any excess of charge resides entirely on its
  surface.
• The electric field just outside a charged
  conductor is perpendicular to its surface.
• On an irregularly shaped conductor, the charge
  accumulates at sharp points.

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Electric Flux
Lets consider a uniform electric field in both
magnitude and direction which penetrates a
surface of area A, perpendicular to the field.
The number of electric field lines N per unit
area A (N/A) is proportional to the field
magnitude (E), E?N/A ? N ? EA.
This quantity is called the electric flux, ?E.
If the surface is not perpendicular to the field,
then ?E EA cos ?, where the normal to the area
A is at an angle ?with respect to the field.
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Electric Flux
If the area is represented by a closed surface,
flux lines passing into the interior of the
volume are negative and those passing outside are
positive.
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Gauss Law
Consider a point charge q at the center of a
sphere of radius r. The electric field magnitude
at any point on the surface of the sphere is
q E ke ?? r2
q ?E EA ke ?? 4?
r2 4? keq r2
The constant ?0 1/ 4? ke is called the
permittivity of free space.
Gauss Law the electric flux through any closed
surface is equal to the net charge inside it
divided by the ?0
?E q / ?0
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Gauss Law
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Summary

• Electric field is a concept, allowing to
  understand the action of the electric force.
• The directions of the electric field at a point
  source is the direction of the electric force
  exerted on a small positive charge.

• Electric flux through a surface is a product of
  the electric field magnitude and the surface area.

• Gauss law allows to calculate the electric flux
  through any closed surface