Download Ch 20 Lecture Notes - University of Colorado Boulder

Ch 20: Electric Charge and Electric Fields
Electric Charge
Experiments involving the rubbing of plastic, glass and wood
rods with wool, silk, and other materials cause the material to
inherit a property that allows for long-range attractive and
repulsive forces.
Examples:
• Unrolling plastic rap
• Running a comb through hair
• Rubbing rubber/plastic/glass rods with fur and silk
• Walking on carpet with slippers
A charged object
always (weakly)
attracts an uncharged
macroscopic object
Pithballs charged by being
touched by same object always
repel
Pithballs can be charged such
that they are attracted to each
other.
Clicker question
Conductors, insulators, and dielectrics
•  Materials in which charge is free to move are conductors.
•  Materials in which charge isn’t free to move are
insulators.
•  Insulators generally contain molecular dipoles, which
experience torques and forces in electric fields.
•  Such materials are called dielectrics.
•  Even if molecules aren’t
intrinsically dipoles, they
acquire induced dipole
moments as a result of electric
forces stretching the molecule.
•  Alignment of molecular
dipoles reduces an externally
applied field.
Visualizing Charge
• 
• 
Charges on an insulator do not move.
Charges on a conductor adjust until there
is no net force on any charge. We call this
electrostatic equilibrium.
Clicker question
A metallic sphere is initially neutral. A negatively charged
rod is brought in contact with a connecting rod, which is
also touching the metallic sphere. What type of rod should
be used such that the metallic sphere is charged?
1.  a conducting rod
2.  a insulating rod
3.  Either kind of rod will charge the sphere.
Clicker question
A negatively charged glass rod is brought near a spherical
conductor, which is initially neutral. The spherical conductor is
initially touching another spherical conductor which is also
initially neutral. While the glass rod is near the conductor, the
two conductors are separated. The glass rod is then removed.
What are the charged states of the two conductors?
1.  Left is positively
charged, right is
negatively charged.
2.  Right is positively
charged, left is
negatively charged.
3.  Left is positively
charged, right is
neutral.
Coulomb’s law and the electric force
•  Like charges repel, and opposite charges attract, with a
force that depends on
•  The product of the two charges
•  The inverse square of the distance between them
•  Mathematically, the electric force is described by
Coulomb’s law:
Clicker question
12
What is the angle between to strings attached to pithballs
of mass m and charge Q?
The superposition principle
•  The electric force obeys the superposition principle.
•  That means the force two charges exert on a third force is just
the vector sum of the forces from the two charges, each treated
without regard to the other charge.
•  The superposition principle makes it mathematically
straightforward to calculate the electric forces exerted by
distributions of electric charge.
•  The net electric force is the sum of the individual forces.
Clicker question
A charge q is to be placed at either A or B on the
mid-line of two charges +q. Will the
force on q be greater at point A or at point B?
A) A
B) B
C) Can't tell without
knowing magnitude
of q.
CT 25.11
Consider the charge configuration shown below.
What is the direction of the net force on
the +q charge?
B
+q
A
C
h
E
s/2 s/2
+Q
+Q
Copyright Univ. of Colorado, Boulder
D
2kqQy
F = 2
(a + y 2 )3/2
The electric field
•  The electric field at a point in space is the force per unit
charge that a charge q placed at that point would
experience:
•  The force on a charge
q in an electric field
is
•  The electric field is
analogous to the
gravitational field,
which gives the force
per unit mass.
Fields of point charges and charge
distributions
•  The field of a point charge
is radial, outward for a
positive charge and inward
for a negative charge.
•  The superposition
principle shows that the
field due to a charge
distribution is the vector
sum of the fields of the
individual charges.
The dipole: an important charge distribution
•  An electric dipole consists of two point charges of equal
magnitude but opposite signs, held a short distance apart.
•  The dipole is electrically
neutral, but the separation of
its charges results in an
electric field.
•  Many charge distributions,
especially molecules, behave
like electric dipoles.
•  The product of the charge and
separation is the dipole
moment: p = qd.
•  Far from the dipole, its
electric field falls off as the
inverse cube of the distance.
Continuous charge distributions
•  Charge ultimately resides on individual particles, but it’s
often convenient to consider it distributed continuously
on a line, over an area, or throughout space.
•  The electric field of a charge distribution follows by summing
—that is, integrating—the fields of individual charge elements
dq, each treated as a point charge:
•  The electric field of an infinite line of charge:
•  The line carries charge density λ (units are C/m):
T 26.11e
What is the vertical component, dEy, of this little "piece"
of Electric field arising from the chunk of length dx?
dE
y=H
x
+ + + + + + + + + + + + + + + + + +dx+ + + ++ +
dEy=
A) |dE|
C) |dE| x/sqrt(H2+x2)
B) |dE| H/(H2+x2)
D) |dE| H/x
E) |dE| H/sqrt(H2+x2)
from CU Boulder
Ey =
�
∞
−∞
kλy dx
(x2 + y 2 )3/2
CT 26.12d
z
A circular ring uniformly charged (charge
Q) is shown.
On the z axis, E = Ez z
ˆ
Which graph correctly represents the
Electric field Ez on the z-axis?
A
C
€
B
y
x
D
from CU Boulder
•  The electric field on the axis of a charged ring:
•  Electric field due to disk of radius R and charge Q (a
distance x from center):
Summary
•  Electric charge is a fundamental property of matter.
•  Charge comes in two varieties, positive and negative.
•  Charge is conserved.
•  The force between two charges is given by Coulomb’s law:
•  The electric force obeys the superposition principle, meaning the
forces due to individual charges sum vectorially.
•  The electric field describes the force per unit charge at a given
point:
•  The field of a dipole follows from Coulomb’s law:
•  The fields of discrete charge distributions are calculated by summation.
•  The fields of continuous charge distributions are calculated by integration.
•  A point charge experiences a force
in an electric field.
•  A dipole experiences a torque in an electric field, and a force if the
field is not uniform.