Download Ch. 18 sec.8,9 - Physics-YISS

18.8 THE ELECTRIC FIELD INSIDE A CONDUCTOR:
SHIELDING
• In conducting materials electric charges move
in response to the forces that electric fields
exert.
• Ex. Suppose a piece of copper carriers a
number of excess –e somewhere within it.
• Each –e would experience a force of repulsion
because of the electric field of its neighbors.
• Since copper is a conductor the –e will move
due to that force.
• They rush to the surface of the copper,
because coulomb’s law is affected by distance
1/r^2.
• Once static equilibrium is established with all
of the excess charge on the surface, no further
movement of charge occurs.
• 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.
• The interior of the copper is electrically
neutral.
• No net electric field because no net
movement of free electrons.
• A equilibrium under electrostatic conditions,
the electric field is zero at any point within a
conducting material.
• Fig 18.30
• Uncharged, solid, cylindrical conductor at
equilibrium in the central region of a parallel
plate capacitor.
• Induced charges on the surface of the cylinder
alter the electric field lines of the capacitor.
• An electric field cannot exist under these
conditions, the electric field lines do not
penetrate the cylinder.
• They end or begin on the induced charges.
• Test charge placed inside the conductor would
feel no force due to the presence of the charges
on the capacitor.
• The conductor shields any charge within it from electric
fields created outside the conductor.
• The shielding results from the induced charges on the
conductor surface.
• Since the electric field is zero inside the conductor,
nothing is disturbed if a cavity is cut from the interior
of the material.
• Stray electric fields are produced by hair dryers,
blenders, vacuum cleaners.
• These stray fields can interfere with the operation of
sensitive electronic circuits; stereo amplifiers, tvs, and
computers.
• To eliminate such interference, circuits are often
enclosed within metal boxes that provide shielding
from external fields.
• Fig. 18.30
• The electric field just outside the surface of a
conductor is perpendicular to the surface at
equilibrium under electrostatic conditions.
18.9 GAUSS’ LAW
• Charge distribution: charges that are spread
out over a region, rather than by a single point
charge.
• Gauss’ law describes the relationship between
a charge distribution and the electric field it
produces.
• Carl Friedrich Gauss, German mathematician.
• Electric flux:
– Using both the idea of electric field and surface
through which field passes.
GAUSS’ LAW ON A POINT CHARGE
• Assume point charge is positive.
• Field line radiate outward in all directions.
• E = kq/r^2, k can be expressed as k = 1/(4πεo),
where εo is the permittivity of free space.
• The equation is:
• We place this point charge at the center of the
imaginary spherical surface of radius r, called
the Gaussian surface.
• A = 4πr^2 so the equation can be written as
EA = magnitude of E of the electric field at any
point on the Gaussian surface and the area A
of the surface.
Electric flux = EA = ϕE
permittivity is the measure of how much
resistance is encountered when forming an
electric field in a medium, permittivity relates
to a material's ability to transmit (or "permit")
an electric field.
Problems take place in a vacuum, this is where
this constant value comes from.
• Form of Gauss’ law that applies to a point
charge.
• Electric flux depends only on the charge q
within the Gaussian surface and is
independent of the radius r of the surface.
•
•
•
•
Using eq. 18.5 to use with arbitrary shapes.
Fig. 18.34
Q = net charge
Any arbitrary shape (doesn’t need to be
spherical)
• Must be closed
• Divided the surface into many tiny sections
with area ΔA1, ΔA2 and so on. Each section is
so small that it is essentially flat and the
electric field is a constant.
• Electric field magnitude is EcosΦ
• Φ is the angle between the electric field and
the normal.
• Electric flux through any one section is then
(EcosΦ)ΔA
• The Electric flux that passes through the entire
Gaussian surface is the sum of all of these
individual fluxes
GAUSS’ LAW
EXAMPLE 15: THE ELECTRIC FIELD OF A
CHARGED THIN SPHERICAL SHELL
EXAMPLE 16: THE ELECTRIC FIELD INSIDE A
PARALLEL PLATE CAPACITOR
Practice Questions
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