Transcript Properties of Electric Charges

Properties of Electric Charges
• There are 2 kinds of electric charge: positive (+) and
negative (–)
– Carrier of positive charge in matter is the proton
(charge = +e)
– Carrier of negative charge in matter is the electron
(charge = –e)
– e = 1.602  10–19 C (typical “shock” experienced on a dry
day transfers about 1  10–9 C)
– Charge is quantized (only comes in integer multiples of e)
• An object becomes electrically charged through
transfer of negative charge (movement of electrons)
– Protons don’t move because they are tightly bound to
atomic nuclei
– Charge is conserved
– Neutral objects have equal amounts of + and – charge
Properties of Electric Charges
• Rubbing a rubber rod with wool transfers negative
charge to rod
– Wool has excess positive charge due to loss of negative
charge
• Rubbing a glass rod with silk transfers negative
charge to silk
– Glass rod has excess positive charge
• Experiments show that:
– Negatively charged rubber rod is attracted to positively
charged glass rod
– Negatively charged rubber rod is repelled by another
negatively charged rubber rod
• Opposite charges attract, like charges repel
Conducting Properties of Materials
• Insulators are materials in which electric charge
does not move easily
– They can be charged, but charge doesn’t move well
– Glass, rubber, plastic, wood, and paper are examples
• Conductors are materials in which electric charge
moves easily
– When an area becomes charged, charge distributes itself
over entire surface
– Copper, aluminum, and silver are examples
– Charge will remain on conductor if you hold it with an
insulator
• Semiconductors are materials that have electrical
properties somewhere between conductors and
insulators
– Silicon and germanium are examples
Methods of Charging/Discharging
• Charging by rubbing
– Increases surface area of contact and enhances charge
transfer
– Works for insulators but not for conductors
• Charging by conduction
– Charged object brought in contact with a neutral object
– Neutral object becomes charged with same sign of charge
as object doing the charging
– Works when (originally) neutral object is insulated
• Discharging by grounding
– Negative charge leaves (or enters) object through
conducting path to Earth or other limitless reservoir of
charge
– Third opening of electrical outlets is the ground (connected
to ground by wire and prevents static charge from building)
Methods of Charging
• Charging by induction (no contact)
– Repulsive force between like charges in
charged rod and (insulated) neutral
conducting sphere causes redistribution of
charge on sphere (figure (b))
– Opposite (like) charges move closer to
(farther from) each other
– Rod would attract sphere
– Induced charge on sphere can remain
if some electrons leave through grounding
– + charge becomes equally distributed
because of high mobility of remaining
electrons
• In insulators, induced surface charges can occur
due to polarization (alignment of molecular charge)
Application: Photocopiers
(from College Physics,
Giambattista et al.)
Coulomb’s Law
• The strength (magnitude) of the attractive or
repulsive force that exists between 2 stationary
charged particles is given by Coulomb’s Law
– |q1| and |q2| are the magnitudes of the charges
– ke = constant = 8.99  109 Nm2 / C2
q1 q2
F  ke
– Applies only to point charges and
r2
spherical distributions of charges
• The direction of the force is always along
a line joining the 2 charges
– Forces are attractive or repulsive depending
on the sign (+ or –) of the charges involved Coulomb's Law
– In agreement with Newton’s 3rd Law: Force
on one charge is equal in magnitude but
opposite in direction to force on other charge
CQ 1: Two particles are held in equilibrium by
the gravitational and electrostatic forces
between them. Particle A has mass ma and
charge qa. Particle B has mass mb and charge
qb. The distance between the charges is d.
Which of the following changes will cause the
charges to accelerate towards one another?
A)
B)
C)
D)
ma is doubled and mb is doubled.
ma is doubled and mb is halved.
qa is doubled and qb is doubled.
d is doubled.
CQ 2: Interactive Example Problem:
The Heart as an Electric Dipole
What is the net electric force exerted by the
dipole charges on Q3 = +3.0 × 10–8 C above
the dipole?
A)
B)
C)
D)
0N
1.3 × 10–5 N to the right
1.3 × 10–5 N up
1.45 × 10–5 N to the right
(ActivPhysics Online Exercise #11.3, copyright Addison Wesley publishing)
The Electric Field
• The influence of gravity on a mass m by another
mass M can be thought of as m immersed in a
gravitational field due to M
g
g
– We can “map” the field by keeping
M
m
m
track of the direction and magnitude
of g at all points
– It is a vector field since it depends on magnitude
& direction

F
– The gravitational field can be written as: g  g
m
• Similarly, the influence of the electrostatic force on a
“test” charge +q0 by another charge Q can be
described by an electric field
– Field “mapped” by direction and magnitude
of E

– Also a vector field
 Fe
– Electric field can be written as: E 
q0
The Electric Field
• The direction of E at a point is the
direction of electrostatic force that
would be exerted on charge +q0 at
that point
• Knowing E at some point, we can calculate Fe on


any charge q0 at that same point from Fe  q0 E
• Since we know the magnitude of Fe from Coulomb’s
q q0
Law, the magnitude of E is given by
Fe
E
 ke
q0
q0 r
– Magnitude of E due to charge q at
position of q0
– Direction of E depends on sign (+ or –) of source
charge q (consistent with above definition)
Mapping Electric Fields
2
 ke
q
r2
Example Problem #15.29
Three identical charges
(q = –5.0 mC) lie along a
circle of radius 2.0 m at
angles of 30°, 150°, and
270°, as shown. What is
the resultant electric field
at the center of the circle?
Solution (details given in class):

Etot  0
E2
E1
30°
E3
Electric Field Lines
• Electric-field patterns can be visualized with electric
field lines
– The way they point indicate direction of E (E is tangent to
electric field lines at each point in space)
– Their spacing gives a general idea of the magnitude of E
• General rules for drawing
electric field lines:
– They begin at positive charges
and end on negative charges
– The # of lines drawn leaving
(ending on) a positive (negative)
charge is proportional to the
magnitude of the charge
– No two field lines can cross each
Electric Field Lines
other
Electric Field Lines
• Two point charges of equal magnitude
but opposite sign form an electric dipole
– # lines that begin at positive charge =
# that terminate at negative charge
– Very near each charge, lines are nearly
radial
– Strong field between the charges
– Electric field generated by Gymnarchus
niloticus resembles that of a dipole
(electrolocation used to spot prey or
predators)
• Electric field lines near 2 equal positive
point charges
– Why is field weak between the charges?
Interactive Example Problem:
Field Lines and Trajectories
Animation and solution details given in class.
(PHYSLET Physics Exploration 23.2, copyright Pearson Prentice Hall, 2004)
Conductors in Electrostatic Equilibrium
• An isolated conductor in electrostatic equilibrium (no
net flow of charge) has the following properties:
– Electric field is zero everywhere inside “meat” of conductor
– Only points on its surface(s) can have a net charge (helpful
while in a car during a thunderstorm)
– Electric field at the surface is
perpendicular to the surface
– Excess charge is more concentrated
at regions of greater curvature, like sharp
points (principle behind use of lightning
rods and electrostatic precipitators)
• Michael Faraday’s famous “ice-pail”
experiment proved that net charge on
conductor in electrostatic equilibrium
resides on its surface
Example Problem #15.35
A –5 mC charge is lowered into the
center of a hollow conductor as shown.
Find the magnitude and sign of the
charge on the inside and outside of the
hollow conductor when the charge is as
shown in Figs. (a), (b), (c), and (d) at
right.
Solution (details given in class):
(a) 0
(b) +5 mC inside, –5 mC outside
(c) 0 inside, –5 mC outside
(d) 0 inside, –5 mC outside
–5 mC
Electric Flux
• When rainwater falls vertically into a bucket, more
(less) rainwater collects in the bucket when its
opening is horizontal (tilted)
– Water “flux” into bucket is maximized when water falls
through cross-sectional area perpendicular to water flow
• The number of electric field lines that pass through
some area perpendicular to the field direction is
proportional to the electric flux FE
F E  EA cosq
– If area A is perpendicular to E, FE = EA,
otherwise we find component of E that is perpendicular to
surface defined by A (E cosq)
– For a closed surface, flux is
positive (negative) if more field
lines leave (enter) than enter
(leave)
Gauss’s Law
• Gauss’s Law relates the electric field on a closed
surface–any closed surface–to the net charge
enclosed by the surface (Qenc)
Q
FE 
enc
– Tells you how much charge you have inside
e0
that “box” without looking inside
– You just need to look at the field lines that enter or exit
the box
– e0 = 8.85  10–12 C2 / Nm2 (“permittivity of free space”)
• Gaussian surfaces are used to make electric field
calculations easy for
symmetrical objects
– Type of surface depends
on symmetry of the
object
Example Problem #15.45
A point charge q is located at the center of a spherical
shell of radius a that has a charge –q uniformly
distributed on its surface. Find the electric field
(a)for all points outside the spherical shell and
(b)for a point inside the shell a distance r from the
center.
Solution (details given in class):
(a) 0
kq
(b) e2 directed radially outward
r
CQ 3: If the distance between a point charge
and an infinitely large charged plate is
increased by a factor of 2, the new force on the
point charge will:
A)
B)
C)
D)
decrease by a factor of 4.
decrease by a factor of 2.
remain the same.
increase by a factor of 2.