Download Chapter 23

Chapter 23
Electric Fields
Intro
• The electromagnetic force between particles
is one of the four fundamental forces of
nature.
• We will begin by discussing electric charges
and the forces associated.
• We will then look at the electric field
produced by a distribution of charges.
• Finally we will examine the motion of a
charged particle in an electric field.
23.1 Properties of Electric Charges
• An object is Electrically Charged if it has an
imbalance between the two fundamental
types of charge.
• Positive and Negative Charges, names given by
Benjamin Franklin are how we identify the
charge of a proton and electron respectively.
• The behavior of charged objects is commonly
observed.
23.1
• Opposite Charges exhibit attractive forces.
23.1
• Similar Charges exhibit repellant forces.
23.1
• Electric Charge is always conserved.
– When one object is rubbed against another,
charge is not created.
– The charged state occurs due to a transfer of
charge from one object to another.
– Whatever one object gains, the other object loses
(for isolated systems).
– Glass/Silk and Rubber/Fur
23.1
23.1
• Charge is quantized
– The fundamental “charge packet” is e.
– All charges represent an integer multiple of e.
q  Ne
– The charges of a proton and electron are +e and -e
respectively.
Quick Quizzes p 709
23.2 Charging by Induction
• Material Classification
– Conductor- material that has free electrons, not
bound to atoms, able to move freely through the
material
• Typically metals- copper, silver, aluminum
• Metallic bonding leaves free electrons
– Insulator- material in which all electrons are
bound to atoms, and cannot freely move.
• Glass, rubber, wood
• Charges remain in a given area, are not free to move
23.2
– Semiconductors- electrical properties somewhere
between conductors and insulators.
• Silicon, Germanium
• The properties can be modified by the addition of
controlled amounts of certain atoms to pure
semiconductors.
• The process is called “doping”
23.2
• Stripping electrons from one material to
another is not the only way to produce a
charge.
• Induction- one process
for charging a conductor.
• Consider a neutral
conducting sphere.
23.2
• A charged rod is brought
near the sphere.
• The sphere is attached
to ground. The excess
electrons flow to ground.
23.2
• Ground- any electron reservoir (a source that
can give/receive electrons freely without
significant change to its overall electrical
characteristics)
• Ex: Earth, Car Frame
23.2
• The ground wire is
removed
• The charged rod is
removed leaving the
conducting sphere with
more positive charge
than negative.
23.2
• Charges can be induced
in insulators even with the
lack of free electrons.
• The molecules can be
realigned in the presence
of an electric charge,
producing a layer of charge
on the surface of the insulator.
23.2
• Quick Quiz p. 711
23.3 Coulomb’s Law
• Charles Coulomb was able
to measure the electric
force between charged
objects using his torsion
balance (very similar in
idea to the Cavendish
Experiment)
23.3
• He was able to verify the following
conclusions about the electric force.
– Follows the inverse square law.
– Proportional the product of the charges q1 and q2
– The force is attractive if charges are opposite sign,
repulsive if they have the same sign.
– The electric force is conservative.
23.3
• Coulomb’s Law determines the electric force
between two point charges.
q1q2
Fe  ke 2
r
• Where ke is the Coulomb constant, q1 and q2
are the particle charges, r is the distance
between them
23.3
• The SI unit for charge, q, is the Coulomb (C)
– 1 C ≈ The charge of 6.24 x 1018 Electrons (e)
– 1 e = 1.602 x 10-19 C
• The coulomb constant
ke  8.9875 x10 N  m / C 
9
2
2
1
4o
• εo is called the Vacuum Permittivity
 o  8.8542 x10 12 C 2 / N  m 2
23.3
• Remember, Force is a vector quantity.
• The force of q1 on q2 is equal and opposite of
q2 on q1
• Quick Quizzes p 712-13
• Examples 23.1-23.4
23.4 Electric Field
• The electric force is a field force
– The force can act through empty space, (like
gravity) no contact is required.
• An electric Field exists in the region
surrounding a charged object.
– This is the source charge.
• When a second charge, is brought into the
field, an electric force acts on it
– This is the test charge.
23.4
• The electric field is defined as the Electric
Force on the test charge per unit of charge.
(N/C)
– Just like gravitational field (the gravitational force
per unit of mass N/kg or m/s2)
Fe
E
qo
g
Fg
m
23.4
• The direction of the Electric Field vector is
determined by which direction the force
would act on a Positive test charge.
– Points away from a positive source charge.
– Points towards a negative source charge.
• The magnitude of the E-Field around any point
source charge can be found by.
qqo
k 2
Fe
E
 r
qo
qo
kq
E 2
r
23.4
• Example 23.5, 23.6
23.5 Electric field from a Continuous
Charge Distribution
• How to we determine the electric field caused
by an object other than a point charge.
• We will look at symmetrical objects on which
the charge is evenly distributed.
• We will “add up” the E-field created by each
“tiny piece” of the charged object.
• We will integrate over the entire charge
distribution.
23.5
• This is a vector operation and direction will
need to be accounted for appropriately.
dq
E  k e  2 rˆ
r
• We will be looking at the charges evenly
distributed on a line, on a surface, or
throughout a volume.
• Charge density will become a convenient
factor.
23.5
• Charge Density
– Volumetric- charge per unit volume (C/m3)
Q

V
– Surface- charge per unit area (C/m2)
Q

A
– Linear- charge per unit length (C/m)
Q


23.5
• When looking at the amount of charge on a
small piece of the object for integration…
– Volume
– Surface
– Line
dq = ρdV
dq = σdA
dq = λdl
23.5
• See Board Diagrams
• Examples 23.7-23.9
23.6 Electric Field Lines
• To Show the electric field pictorially, electric
field line diagrams can be drawn.
• The Electric Field vector E is tangent to the
field line at any point.
• The number of field lines through a surface
per unit area is proportional to the magnitude
of the electric field in that region.
23.6
• On a positive point charge– The electric field lines radiate
outward in all directions
– In 3D, the distribution is
spherical.
– A positive test charge would
be repelled from the source
charge.
23.6
• On a negative point charge– The field lines radiate inward
in all directions.
– A positive test charge would
be attracted to the source
charge.
23.6
• For an electric Dipole (equal/opposite
charges)
– The number of field
lines leaving the
positive charge
equals the number
of field lines
terminating on the
negative charge.
23.6
• Equal and Like Charges
– The same number of
charges leave both particles.
– At a great distance
the field approximates
to that of a single 2q charge.
23.6
• Opposite/Unequal Charges
– The number of lines
leaving/terminating
each charge is proportional
to their relative charges
(in this case, 2 to 1)
– At a great distance the
E field would approximate
to that of a single charge q.
23.6
• Drawing Electric Field Lines
– The lines must begin on a positive charge and
terminate on a negative charge.
• With a charge imbalance, some lines will begin/end
infinitely far away.
– The number of lines beginning/terminating is
proportional to the relative charges.
– The fields lines can not cross.
• Quick Quizzes p 725
23.7 The Motion of Charged Particles
in an Electric Field
• A charged particle in an electric field
experiences an Electric force.
• If this is the only force acting, Fe is the net
force.
• The charged particle will accelerate according
to Newton’s 2nd Law
Fe  qE  ma
23.7
• If E is uniform, then a is a constant value.
– If the charge is positive, the acceleration vector
points with the E-field.
– If the charge is negative, the acceleration vector
points against the E-field.
• Since acceleration is constant, kinematics
equations can be use.
• Example 23.10 p 726
23.7
• Charged Projectiles– The charged particle can follow a 2D projectile
path if it has velocity perpendicular to the E-field.
– Example
23.11 pg 727
23.7
• The Cathode Ray Tube (CRT)
– Used for display of electronic information
• Oscilloscopes, Radar systems, TV/Computer Monitors