Electric Potential
•
Electric fields are
responsible for another
type of potential energy.
Charges can move “uphill” or
“downhill” in the field.
•
Energy is stored in the
arrangement of charges.
Capacitors can store a lot of
energy that can be quickly
discharged.
•
Muscle and nerve cells
have large electric fields.
Depolarization of nerve and
muscle cells produces externally
measurable fields.
Day 1
Pushing a Stone Uphill
Suppose you need to roll a stone to the top of a hill.
• What factors determine how much force you need to apply?
• What factors determine how much work you need to do?
Sketch a graph of the potential energy vs. distance for a
ball slowly rolled up the slope.
Sketch a graph of the potential energy vs. distance for a positive
charge moved from the negative plate to the positive plate.
U
+
-
+
-
+
-
+
-
+
-
+
-
+
-
Electric Potential Energy
+
E=100
N/C
A +1 nC charge is at rest in
the earth’s field of 100 N/C,
directed down.
1m
+
Raising this charge by 1 m
means doing 1x10-7 J of work.
+1 nC
What is the increase in potential energy?
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B. !
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D. !
0.5x10-7 J
1x10-7 J
2x10-7 J
4x10-7 J
Electric Potential Energy
+
+
E=100
N/C
1m
1m
+
+
+1 nC
+2 nC
Raising the +1 nC
charge by 1 m
increases potential
energy by1x10-7 J.
What is the increase in potential energy when a +2 nC
charge is raised by 1 m?
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B. !
C. !
D. !
0.5x10-7 J
1x10-7 J
2x10-7 J
4x10-7 J
Potential Difference
How high is the hill?
The potential difference is the change
in potential energy “per charge”:
ΔV =
ΔU elec
q
Units: J/C, or volts (V).
The difference in potential ∆V can be called a voltage.
Potential Difference
+
+
E=100
N/C
1m
1m
+
+
+1 nC
+2 nC
Raising the +1 nC
charge by 1 m
increases potential
energy by1x10-7 J.
Raising the +2 nC
charge by 1 m
increases potential
energy by 2x10-7 J.
What is the difference in potential between the two
points?
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B. !
C. !
D. !
50 V
100 V
200 V
400 V
Potential & Potential Energy
The change in potential energy
when a charge goes through a
potential difference ∆V:
ΔU elec = qΔV
Each second, 0.30 C of charge moves
from the negative terminal of a
battery to the positive terminal; the
increase in potential is 1.5 V.
How much chemical energy is
required each second?
1
1
1
1
1
1
2
1
In the flashlight battery, 0.30 C of charge moves from the
negative terminal of a battery to the positive terminal
each second; the increase in potential is 1.5 V.
What is the power?
Connecting Field and Potential, Part I:
In a uniform field, moving
a distance ∆d produces a
change in potential:
ΔV = E ∆ d
The field depends on the
change in potential:
E=
ΔV
Δd
• We’ve expressed field values in N/C.
• Another unit for electric field is V/m.
• A large field means a rapid change in
potential.
Analogies
Potential difference:
How high is the hill?
V=
U elec
q
Electric field:
How steep is the
slope?
E=
ΔV
Δd
A 1.8-m-tall man steps outside; the electric field is
directed downward, and has magnitude 100 N/C.
What is the potential difference between the position of
his head and the position of his feet?
Equipotential and Field
Assume that the electric field is uniform between the two spheres.
When a spark jumps, we can assume that the field is 1x106 V/m.
1. What is the potential difference between the two spheres? This
is “the voltage of the Van de Graaf generator”.
2. A typical charge on the sphere is 10 µC. If we could transfer
this charge without changing the potential difference, what
would be the change in potential energy?
Visualizing Potential
Connecting Field and Potential, Part II
A conductor has zero field inside, so is an equipotential.
Sketch:
1. field lines
2. equipotential lines
for the region between the two parallel plates with
opposite charges.
Plates are
infinite, of
course.
Sketch:
1. charges on the conductor
2. equipotential lines
3. field lines
for the region between the two parallel plates
Now add a conducting box
Atmospheric electricity
+
_
+
+
+
+
+
+
+
+
_
_
_
+
+
+
_
+
_
_
+
+
The bottom of a cloud (in blue) has a uniform positive charge and
is at a constant potential. The ground below (in green) is a good
conductor, so an opposite negative charge will collect here.
Draw field lines and equipotential lines, and note:
1. At which of the noted points is the field the strongest?
2. At which of the noted points is the potential the highest?
1.Connect a
battery to a
pair of
plates.
3.This creates a
potential
difference...
4....which
creates a
field...
5....which
exerts forces
on charges.
2.Charges move.
++++++
∆V
E=
______
ΔV
Δd
∆d
++++++
E
______
F
F = qE
-
The figure
Warming up
The bottom of a cloud (in blue) has a uniform positive charge and
is at a constant potential. The ground below (in green) is a good
conductor, so an opposite negative charge will collect here.
Draw field lines and equipotential lines, and note:
1. At which of the noted points is the field the strongest?
2. At which of the noted points is the potential the highest?
Each part of the figure
Warming up
A
B
What is the potential difference between points A and B?
If lightning deposits a large charge in a small area, sketch
the resulting equipotentials around the charge center.
An echo from General Physics I...
Scenario: The Datsun on the Hill
When I taught in Swaziland, I had a rather
dilapidated Datsun that wouldn’t start with the
starter motor. It would only start if the clutch was
popped at a minimum speed of about 4.5 m/s.
The best approach was to park on a hill. What is
the minimum possible height of hill that would do
the trick?
The electron gun in a CRT
television works like this:
A filament heats up, and electrons
come off. The filament is grounded;
its potential is 0 V.
At some distance, a metal plate
with an aperture is set at a
potential of 150 V.
The electron accelerates toward
the positive plate, then continues
through the aperture.
1. What is the direction of the electric field between the
filament and the plate?
2. How fast is the (initially stationary) electron moving when it
gets to the plate?
How much kinetic energy?
How much kinetic energy?
100 V
How much kinetic energy?
500 V
Charging a Capacitor
Charges flow
∆VC
∆VB
Capacitor Formulas
Unit: farad, F:
The flash unit in a camera creates a very short but very bright flash:
105 W for a time of 10 µs. The flash is produced by a 22 µF capacitor.
To what voltage must the capacitor be charged?
the figure.
Warming up
A. Increase / Greater
B. Same
C. Decrease / Less
capacitor. What is the impact speed of the proton?
b. What is its kinetic energy, in joules?
70. ||| A proton is released from rest at the positive plate of a paralc. lel-plate
What iscapacitor.
its speed?
It crosses the capacitor and reaches the nega8. |||||tive
What
potential
difference
is needed
to will
accelerate
a He + ion
plate with a speed
of 50,000
m/s. What
be the proton’s
6
y
(charge
+e, mass
4 u) from rest
to a speed
1.0 *the10amount
m/s?
final speed
if the experiment
is repeated
withof
double
ge
9. || An
electron
with capacitor
an initialplate?
speed of 500,000 m/s is brought to
of charge
on each
rest|| by
electric
71.
Theanelectric
strength
is -27
20,000
V/m inside a parallel1 ufield
=field.
1.66
× 10
kilograms
withmove
a 1.0 mm
released or
a. plate
Did capacitor
the electron
intospacing.
a regionAnofelectron
higherispotential
-19 J
1
eV
=
1.6
×
10
from
rest
at
the
negative
plate.
What
is
the
electron’s
speed
lower potential?
when
it
reaches
the
positive
plate?
b. What was the potential difference that stopped the electron?
72.
In thewas
early
Millikan
small
charged in
drop
c. ||What
the1900s,
initialRobert
kinetic
energyused
of the
electron,
eleclets
of
oil,
suspended
in
an
electric
field,
to
make
the
first
quantitatron volts?
tive measurements of the electron’s charge. A 0.70-μm-diameter
10. ||| A proton with an initial speed of 800,000 m/s is brought to
droplet of oil, having a charge of +e, is suspended in midair
.61?
restbetween
by an electric
field. plates of a parallel-plate capacitor. The
two horizontal
a. upward
Did theelectric
proton
move
intodroplet
a region
of higher
potential
force
on the
is exactly
balanced
by the or
t follower
potential?
downward force of gravity. The oil has a density of 860 kg/m3,
prob. and
What
the potential
stopped
proton?
thewas
capacitor
plates difference
are 5.0 mmthat
apart.
Whatthe
must
the
c. potential
What was
the
initial
kinetic
energy
of
the
proton,
in
electron
difference between the plates be to hold the droplet
in
A
equilibrium?
volts?
B.
73. |||| Two 2.0-cm-diameter disks spaced 2.0 mm apart form a
parallel-plate capacitor. The electric field between the disks is
5
a Section5.0
* 10
V/m.
21.4
Calculating
the Electric Potential
ce v0
a. What is the voltage across the capacitor?
11. || The
electric
point
that is halfway between two
b. How
muchpotential
charge is at
onaeach
disk?
In a photoelectric
effect
experiment,
shining
ultraviolet
onaa
identical
charged
particles
is
300
V.
is the
potential
c. An electron is launched from the What
negative
plate.
It light
strikesat
C
7
metalpoint
surface
causes
electrons
to
be
ejected
from
the
surface
thatpositive
is 25%plate
of the
from
one*particle
the other?
the
at way
a speed
of 2.0
10 m/s.toWhat
was the at a
5
speed
movehas
toward
12. || of
A 2.7x10
2.0
cm *m/s.
2.0The
cmas ejected
parallel-plate
capacitor
a 2.0anmm
electron’s
speed
it left theelectrons
negative
plate?
electrode
aelectric
few mm
away.
a potential
difference
74.
|| Inlocated
proton-beam
therapy,
a Applying
high-energy
beam
of
protons is
spacing.
The
field
strength
inside
the
capacitor
ts
fired
at a tumor.
come to rest
in the
between
surfaceThe
andprotons
the electrode
causes
thetumor,
electrons
1.0is*the
105metal
V/m.
their
kineticWhat
energypotential
and across
breaking
thewill
tumor’s
nitialto speed
up or
down.
difference
cause
a. depositing
What
is slow
the
potential
difference
theapart
capacitor?
DNA,
thus
killing
its
cells.
For
one
patient,
it
is
desired
that
as itthe electrons
to come
to isrest
they reach the electrode?
b. How much
charge
on just
eachas
plate?
0.10
J
of
proton
energy
be
deposited
in
a
tumor.
To
create
the
13. ||| Two 2.00 cm * 2.00 cm plates that form a parallel-plate
proton beam, the protons are accelerated from rest through a 10
20
V
ncapacitor are charged to {0.708 nC. What are the electric
MV potential difference. What is the total charge of the protons
field
field
strength inside and the potential difference across the
that must be fired at the tumor to deposit the required energy?
V,
h the
of
u
capacitor if the spacing between the plates is (a) 1.00 mm and
(b) 2.00 mm?
18/09/13 2:42 PM
18/09/13 2:42 PM
Dielectrics
Touch screens use variable capacitors.
Touch one with a pen. What happens?
Cell #1
Conducting
Fluid
Insulating
Membrane
Conducting
Fluid
Cell #2
The Cell Membrane Works
as a Capacitor Too
The Dipole Moment
p
A dipole lines up with a field
Each part of the figure
Remember...
Dipole Potential
The Electric Field of the Cell Membrane
The potential inside a
cell is 70 mV lower than
the potential outside the
cell.
This potential difference
is created by charges on
the cell membrane.
If the membrane has a
thickness of 7.0 nm, what
is the electric field inside
the membrane?
Depolarization
-
+
+
+
+
-
-
The electric field of the heart
Electrical sense in sharks and rays
Ampullae of
Lorenzini
These organs sense differences in potential as small as 5 nV.
A shark senses a difference in
potential between two points.
Use a mathematical expression
to explain why having a wide
head allows a shark to sense a
smaller electric field.
652
C H A P T E R 20
Electric Fields and Forces
heart is a large electric dipole. The o
during each beat of the heart as the de
The electric dipole of the heart g
(a)the
Thewide
electric
dipole of the heart
Why
head?
throughout the torso, as shown in FIG
652
20 Electric Fields and Forces
A cross section of
This line separates
electrocardiogram measures the chang
the heart
showingThe beating
cells
that haveheart is a large electric
FIGURE 20.34
heart
dipole. The orientation and strength of the dipole c
generates
field.
muscle
tissuea dipole electric depolarized
and
heart’swave
electric
can
during each beatsurement
of the heart asof
the the
depolarization
sweeps field
across it.
The beating heart
generates a dipole electric field.
FIGURE 20.34
CHAPTER
those that have not.
The electric dipole of the heart generates a dipole electric field that e
(a) The electric dipole of the heart
Depolarized
throughout the torso, as shown in FIGURE 20.34b . As we will see in Chapter
section of
This line separates
tissue Athecross
electrocardiogram measures the changing electric field of the heart as it beats
heart showing
cells that have
muscle tissue
Depolarized
tissue
STOP
TOfield
THINK
20.6to diagnose
Which
of the
f
surement of the heart’s
electric
can be used
the operation
of the
depolarized and
those that have not.
electric field created by two positive c
Which of the following is the correct representation
electric field created by two positive charges?
STOP TO THINK 20.6
21.7 Capacitance and Capacitors
Tissue
not yet
Tissue not yet
depolarized
depolarized
FIGURE 21.28 Measuring an EKG.
ectric potential of the heart is an invaluable diagnostic
nly potential differences are meaningful, so we need to
rence between two points
on the
torso. atInthepractice,
as
Many electrodes are
The charge
separation
line between
attached to the torso.
ential difference is measured
between
several
pairs
of
the two regions creates an electric dipole.
The
charge differences
separation
at theasline
ds). A chart of
the potential
is known
an between
(b)
The
fieldEuropean
of the
heartorigin,
in the
the or,
two
regions
creates
anbody
electric
dipole.
iated either ECG
from
its
EKG.
A
ing an EKG uses 12 leads and records 12 pairs
of potenA.
The heart’s dipole
685
B.
C.
D.
field extends
(b)
The field of themeasurement
heartthroughout
in the
body
lified model
of electrocardiogram
using
the
torso.
on each arm. As the wave of depolarization moves
A.
B.
ring each heart beat, the dipole moment vector The
of theheart’s dipole
e and direction. As Figure 21.29 shows, both of these
field extends
Consider a conductor in electrostatic equilibrium (recall that this means tha
nce between the electrodes, so each point on the EKG
∆V
of
charges are moving). Suppose there were an electric field inside th
thethetorso.
particular magnitude and orientation of the throughout
dipole
20.6 Conductors and Electric Fields
ductor. Electric fields exert tforces on charges, so an internal electric field
Records of the potential differences between
exert forces on the charges in the conductor. Because charges in a conduc
various pairs of electrodes allow the doctor
free to
these forces would cause the charges to move. But that wou
to analyze
the move,
heart’s condition.
ference between the electrodes changes as the heart beats.
(b)
(c)
FIGURE 20.35 The electric field inside and
outside a charged
conductor.
Septal depolarization
Ventricular
depolarization
(a) The electric field inside
the conductor is zero.
20.6
Conductors
and
late the assumption that all the charges are at rest. Thus we’re forced to co
the electricConsider
field is zero at
points inside in
a conductor
in electro
a all
conductor
electrostatic
equilibrium.
record of the potential
of the
are moving).
Supposei
BecauseThe
the
electric
fieldcharges
inside a conductor
in electrostatic equilibrium
difference between the two
any excesselectrodes
charge on
the conductor must lie at its surface, as shown in FIGURE
is the
ductor. Electric fields exert forces on
electrocardiogram.
Any
in the interior of the conductor would create an electric field th
= V2charge
- V1
∆V
violation of our exert
conclusion
that the field
is zero. Physically,
excess
forces
on inside
the charges
in the
co
ends up on the csurface because the repulsive forces between like charges caus
free
to move,
forces
would cau
to move as far apart
as possible
without these
leaving the
conductor.
FIGURE 20.35b shows that the electric field right at the surface of a charge
late the assumption that all the charg
a
u
ductor is perpendicular to the surface. To see that
this is so, suppose E had
u
(d)
that
t
Field of the Heart
The
Electrocardiogram
Positive or negative?
Big or small?
A
B
C
Positive or negative?
Big or small?
A
B
C
Positive or negative?
Big or small?
A
B
C
Direction of
dipole moment?
+ 3.0 mV
+ 4.0 mV
+ 2.0 mV