Physics 219 Spring 2013 - Help Center Schedule, Room 11
Radu Marius : Friday 10:30 AM – 12:00 PM
Darren Erdman: Friday 12:00 PM – 1:30 PM
Radu Marius : Friday 10:30 AM – 12:00 PM
Darren Erdman: Friday 12:00 PM – 1:30 PM
Additional schedules will
be filled by next week
Chapter 17 Electric Forces and Fields – Lecture 2
17.1 Evidences for Electric Forces:
The Observational Facts
17.2 Electric Forces and Coulomb’s Law
17.3 The Electric Field
17.4 Conductors, Insulators, and the Motion of Electric
Charge
17.5 Electric Flux and Gauss’s Law
Electric Field
• An electric field gives
another explanation of
electric forces
• The presence of a
charge produces an
electric field
• Shown by the arrows in
the figure
• The electric field is
similar to the
gravitational field near
an isolated mass
Section 17.3
Electric Field, cont.
• A positive charge
produces field lines that
radiate outward
• For a negative charge
the field lines are
directed inward, toward
the charge
• The electric field is a
vector and denoted by E
Section 17.3
Electric Field and Test Charge
• Consider a point in
space where the electric
field is E
• If a charge q is placed
at the point, the force is
given by F  q E
• The charge q is called
a test charge
• By measuring the force
on the test charge, the
magnitude and direction
of the electric field can
be inferred
Section 17.3
Electric Field, cont.
• The electric force is either parallel or antiparallel to
the electric field
• Parallel if q is positive (+), and antiparallel (-) if q is
negative
• SI units of the electric field are N/C
• Coulomb’s Law can be used to find the magnitude
of the electric field, where Q is the charge producing
the field and q is the test charge
kQq
F
F  2  qE
 E
r
q
kQ
E 2
r
Section 17.3
Electric Field, final
• The direction of the electric field is along the line
connecting the charge producing the field to the
point where the field is measured
• The electric field is directed away from Q when Q is
positive
• The electric field is directed
inward toward Q when Q is
negative
Section 17.3
Importance of the Electric Field
• An electric field is present even when there is no
second (or test) charge present to experience the
electric force
• Any charge or collection of charges will produce an
electric field
• The electric field helps explain how the Coulomb
force can act between two charges that are
separated by large distances
• The electric field is essential for understanding
electromagnetic waves
Section 17.3
Drawing Electric Field Lines
• Another way to visualize an
electric field is with electric
field lines
• Field lines are a set of
continuous lines that are
always parallel to the electric
field
• Field lines must always begin on positive (+) charges
• Field lines must always end on negative (-) charges
• Electric fields also obey the superposition principle
• When adding the fields from multiple charges, always
add them as vectors
Section 17.3
Examples of Electric Field Lines
• The plot of the field lines does not show the
magnitude of the field directly
• Changes in field strength can be inferred from the
spacing of the field lines
• The lines are most closely spaced where the field is
the largest
Section 17.3
Inverse Square Laws, cont.
• The electric field lines
emanate outward from
a point charge
• They intercept larger
and larger surface
areas
• The surfaces are
spherical
• Their areas increase as
A r2
• The number of field
lines per unit area falls
as 1/r2
Section 17.3
Electric Fields and Multiple Charges
Example 17.5
• To find the electric field due to multiple charges use
the principle of superposition
• Find the electric fields due to each charge
• Add them as vectors
Section 17.4
Electric Field (Review)
The net Coulomb force on a given charge is always
proportional to the strength of that charge.
Define Electric field, which is independent of the test
charge, q, and depends only on position in space:
F
E
q
N V 
  
 C m
Electric Field due to a
Point Charge Q
F
1 Q
Q
E 
rˆ  k 2 rˆ
2
q 4 0 r
r
qQ
 F  k 2 rˆ
r
E points away from positive charges
and toward negative charges.
Charging an Insulator
• A few electrons are
placed on the insulator
• They will tend to stay
where they are placed
• The insulator will
eventually be
neutralized
• The excess electrons
will attract free ions
from the air
• They will neutralize the
original charge
Section 17.4
Excess Charge on a Metal
• Electrons can move easily
through a metal
• Excess electrons will be
distributed on the surface of the
metal (A)
• Excess positive charges (postive
ions or lack of electrons) will be
distributed on the surface of the
metal (B)
• In all cases, the electric field is
zero inside a metal in static
equilibrium (C)
Section 17.4
Charging an Object by Rubbing
+q
- -+ 0 +
++ +
Polarization
• The act of rubbing causes some charge to be
transferred from one material to another
• Example: when rubbing amber with fur, electrons are
moved from the fur to the amber
• The amber acquires a net negative charge
• The fur is left with a net positive charge
• Applies to many combinations of materials
Section 17.4
Polarization
• The rod and paper are both neutral
• The rod is rubbed by the fur, obtaining
a negative charge
• The presence of the rod causes the
electrons in the paper to be repelled
and the positive ions are attracted
• The paper is said to be polarized
- -+ 0 +
+q
++ +
Polarization
Section 17.4
Polarization, Balloon and Water Example
Section 17.4
Electric Dipoles in Nature
• Typical dipole consists of positive and
negative charges slightly displaced.
• Water molecule can be thought of
as consisting of 2 standard dipoles at
an angle to each other.
 Net neutral molecules can have
electrical dipole moments
 Permanent dipole moment (polar)
vs. induced dipole moment
The Van de Graaff Generator
Figure 17.22
A Van de Graaff generator
produces a large electric charge
by rubbing an internal rubber
belt. This belt transfers electric
charge to the metal sphere at
the top of the generator.
Figure 17-22 p560
The Van de Graaff Generator
The Van de Graaff generator was invented by Robert J. Van de Graaff,
an American physicist (1901-1967)
• The Van de Graaff generator
works by applying a positive
charge to a non-conducting
moving belt using a corona
discharge
• The moving belt driven by an
electric motor carries the charge
up into a hollow metal sphere
where the charge is taken from
the belt by a pointed contact
connected to the metal sphere
• The charge that builds up on the
metal sphere distributes itself
uniformly around the outside of
the sphere
• For this particular Van de Graaff
generator, a voltage limiter is
used to keep the Van de Graaff
generator from producing sparks
larger than desired
Demo - Electroscope
Supplemental Material
Conductors
• Each atom by itself is
electrically neutral
• Equal numbers of
protons and electrons
• This example is copper
• When these atoms come
together to form the
piece of metal, electrons
are freed
29Cu,
A=Z+N=63, 65
Z=29 Section 17.4
Conductors, cont.
• These electrons move freely through the entire piece
of metal
• These electrons are called conduction electrons
• The electrons leave behind positively charged ion
cores that are bound and not mobile
• A piece of metal can also accept extra electrons or
release some of its conduction electrons so the
entire object can acquire a net positive or negative
charge
Section 17.4
Insulators
• In insulators the electrons
are not able to move freely
through the material
• Examples include quartz,
plastic and amber
• This example is quartz (SiO2)
Section 17.4
Insulators, cont.
• Electrons cannot escape from these ions
• There are no conduction electrons available to carry
charge through the solid
• If extra electrons are placed on an insulator, they
tend to stay in the place where initially placed
Section 17.4
Liquids and Gases
• The total charge is zero
and the sample is
neutral
• A few molecules always
dissociate into free ions
• These ions can carry
charge from place to
place similarly to the
conduction electrons
• This example is water,
but gases are similar
Section 17.4
Quiz 1 (Chapter 17)
Three charges +q, +Q, and –Q are placed at the
corners of an equilateral triangle as shown. The
net force on charge +q due to the other two
charges is
A.up.
B.down.
C.along a diagonal.
D.to the left.
E.to the right.
Quiz 1 (Chapter 17)
Three charges +q, +Q, and –Q are placed at the
corners of an equilateral triangle as shown. The
net force on charge +q due to the other two
charges is
A.up.
B.down.
C.along a diagonal.
D.to the left.
E.to the right.