Transcript Electric Field Lines - a “map” of the strength of the

Electric Field Lines - a
“map” of the strength of
the electric field. The
electric field is force per
unit charge, so the field
lines are sometimes
called lines of force.
Electric field lines are
always directed away
from positive charges and
toward negative charges.
Where lines are closest
together, the electric field
is strongest.
Where the electric
field lines are equally
spaced, the electric
field has the same
strength at all points.
Two separated point
charges that have
the same magnitude
but opposite signs
are called an electric
dipole.
The electric field of a
dipole is proportional to the
product of the magnitude of
one of the charges and the
distance between the
charges. This product is
called the dipole moment.
Electric field lines always begin
on a positive charge and end on
a negative charge and do not
start or stop in midspace.
Also, the number of lines
leaving a positive charge
or entering a negative
charge is proportional to the
magnitude of the charge.
Field lines never
cross, because
at any one point
there is only one
value for the
electric field.
Excess electrons within a
conductor are repelled by
all electrons in the material.
Due to the distance factor
2
of Coulomb’s law, 1/r , they
rush to the surface of the
conductor.
They spread out evenly
over the surface (They
repel each other also).
An excess positive
charge also moves
to the surface of a
conductor.
At equilibrium
under electrostatic
conditions, any excess
charge resides on the
surface of a conductor.
Free electrons within the
conductor are not moving,
so no electric field exists
there. At equilibrium under
electrostatic conditions, the
electric field at any point
within a conducting material
is zero.
Additionally, the conductor
shields any charge within it
from electric fields created
outside the conductor.
Electronic circuits are often
protected from “stray” electric
fields by metal containers.
A conductor alters the
electric field around it.
The electric field just outside
the surface of a conductor is
perpendicular to the surface
at equilibrium under
electrostatic conditions.
If the field were not
perpendicular, there would be
a component parallel to the
surface which would make the
free electrons move over the
surface; but the electrons do
not move, so the field must be
perpendicular.
An electric field is
sometimes produced by
charges spread out over a
region, not by a single
point charge. An extended
collection of charges is
called a charge distribution.
Gauss’ law describes the
relationship between a
charge distribution and
the electric field it
produces.
Gauss law for a point
charge is: EA = q/ε0
EA = q/ε0
E is electric field magnitude
A is the area of the surface
q is the charge in coulombs
ε0 is the permittivity of free
space
The product of electric field
magnitude E and the area of the
surface A, EA is called the
F = EA
electric flux, FE.
.
E
This definition for flux only
works for a point charge and a
spherical Gaussian surface.
The Gaussian surface can
have any arbitrary shape,
but it must be closed.
The field direction is not
necessarily perpendicular
to the surface.
The magnitude of the
electric field need not
be constant on the
surface, it can vary
from point to point.
By dividing the surface into
many small sections, finding
the flux for each section, and
adding them together, the
total flux of the surface can
be found.
FE = ∑(E cosf)∆A
Gauss’ law relates
the electric flux FE to
the net charge q
enclosed by the
arbitrarily shaped
Gaussian surface.
Gauss’ law
The electric flux through a
Gaussian surface is equal to the
net charge q enclosed by the
surface divided by the ε0 , the
permittivity of free space:
FE = ∑(E cosf)∆A = q/ε0.
The SI unit of electric flux: N•m2/C
Ex. 14 - A thin spherical shell
has radius R. A positive
charge Q is spread uniformly
over the shell. Find the
magnitude of the electric field
at any point (a) outside the
shell and (b) inside the shell.
Ex. 15 - Use Gauss’ law to
prove that the electric field
inside a parallel plate
capacitor is constant and
has a magnitude E = s/ε0.
s is the charge density on
a plate.