Transcript The Electric Field

Lecture 2
The Electric Field.
Chapter 15.4  15.9
Outline
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The Concept of an Electric Field
Electric Field Lines
Electrostatic Equilibrium
Electric Flux and Gauss’ Law
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.
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.
The Electric Field
Once the electric field is known at some point, the electric
force on any charge q0 placed at that point is:
F = q 0E
|Q|
E = ke 
r2
|Q| |q0|
F = 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.
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.
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.
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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.
Electric Flux
Let’s 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.
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.
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 ke|q|
r2
The constant є0 = 1/ 4 ke is called the permittivity of
free space.
 E = q / є0
Gauss’ Law: the electric flux through
any closed surface is equal to the net
charge inside it divided by the є0
Gauss’ Law
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