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§16.5 Motion of a Point Charge in
a Uniform E-Field
Q) What is E-field around a
metal plate w/ +Q?
+
+
+
Q) A metal plate
w/ –Q?
+
1
Parallel metal plates  uniform E
Fig. 16.34
Charge +q
& mass m
“Cathode Ray Tube” (TV)
“Electron gun”
q
a E
m
E
Charge +q
& mass m.

v  at
x  12 (v f  v i )t
Use kinematic equations
w/ constant a from Ch. 4:
x  v it  12 at 2
v 2f  v i2  2ax
4
Example: What electric field is needed to keep an
electron suspended in the air against gravity?
(a) Direction?
(b) Strength?
(c) Would a proton require the same field?
Example (PP 16.48): An electron is placed in a
uniform electric field of strength 232 N/C. If the
electron is at rest at the origin of a coordinate
system at t = 0 and the electric field is in the
positive direction, what are the x- and y-coords
of the electron at t = 2.3 ns? The velocity?
5
§16.6 Conductors in Electrostatic Equilibrium
• Conductors are easily polarized: free electrons move
around freely inside the material.
• Any charges placed on a conductor will arrange themselves
in a stable, unmoving distribution: electrostatic equilibrium.
• For a conductor in electrostatic equilibrium:
1) The E-field inside it is zero (no field lines)
2) Any net charge must reside on the surface
3) Just outside the surface, E is perpendicular to the surface
4) Any excess charge will accumulate where the surface is
highly curved (i.e. a sharp point): E is strongest there.
6
Put 16 nC on the following surface:
Q) Where will charges go?
Q) What will the E-field look like?
Lightning rod
7
Chapter 18: Electric Potential
• Electric Potential Energy
• Electric Potential (Voltage)
• How are the E-field and
Electric Potential related?
• Motion of Point Charges in
an E-field
• Capacitors
• Dielectrics
More help: SPS drop in
MW 8:30-9:30am
Canvas goodies
TR 11am-noon
178 Overman Hall
For Wed recitation:
• do Online Problems (WA)
• do Practice Problems:
Ch 17 #45, 87
Ch 18 tbd
Lab: 2.03 (vsound) this week
• Read instructions
• Do Pre-Lab & turn in
• Quiz #1 (Ch 13, 17, 18)
Wed Sep 18 during
recitation (indiv, group)
8
§17.1 Electric Potential Energy
Electric potential energy (PEe) is:
• energy stored in the electric field,
kq1q2
PE e 
r
• work (W=F.d) done to put charges in place.
PE g  mgh

+Q
+Q
h
m
+q
-q
9
Example: Two point charges, Q = +6.0 mC
and q = +5.0 mC are separated by 15.0 m.
(a) What is their potential energy?
(b) If Q is fixed and q is free to move, what
will q do?
(c) How does q’s motion affect the potential
energy? Explain in terms of conservation
of energy.
10
Q) What is the potential energy of three point
charges arranged as a right triangle?
kq1q2
PE12 
r12
q2
r23
r12
q1
kq1q3
PE13 
r13

q3
r13
kq2q3
PE 23 
r23

Q) What if there are four charges?

PEtot  PEi  PE12  PE13  PE23  ...
(scalar sum)
11
§17.2 Electric Potential
Electric potential is the electric potential energy
per unit charge:
PE e
V
qtest
For a point charge Q:

• scalar
• 1 V = 1 J/C.
PE e kQ
V

qtest
r
When a charge q moves through a potential
difference of V, its potential energy change is

PEe = qV.
12
Example: A charge Q = +1 nC is placed somewhere in
space far from other charges. Take ra = rb = rc = rd = 1.0 m
and re = rf = rg = 2.0 m.
f
(a) Compare the potential
at points d and g.
b
c
e
a
Q
d
g
(b) Compare the potential at points a and b.
13
Example: A charge Q = +1 nC is placed somewhere in
space far from other charges. Take ra = rb = rc = rd = 1.0 m
and re = rf = rg = 2.0 m.
(c) Place a charge of +0.50 nC at
point e. What will the change in
potential (V) be if this charge is
moved to point a?
f
b
c
e
a
Q
d
g
(d) What is the change in potential energy (PE) of the
+0.50 nC charge ?
14
§17.3 The Relationship between E and V
Equipotentials:
surfaces of equal
potential.
f
b
c
e
a
Q
+9 V
+4.5 V
d
g
15
E points in direction of maximum potential decrease.
E is perpendicular to the equipotential surfaces.
f
b
c
E
e
a
Q
+9 V
+4.5 V
d
g
Q) What is V at 3m?
At 0.5 m?
16
Fig. 17.19
Q: What do the equipotentials look like around a – charge?
Equipotentials
and field lines
for a dipole:
18
Uniform E-field:
V1
V2
V3
V4
E
Equipotential surfaces
U e
V 
  Ed
q
Where d is the distance
over which V occurs.
19
Example: Two parallel plates are separated by 2.0 mm.
One is at a potential of 3000.0 V while the other is at 0.0 V.
What is the E-field between them?
Q) Why is E negative?
20
Hollow Conducting Sphere (radius = R):
(Similar
for other
hollow
shapes)
Van de Graaff
generator
22
§17.4 Moving Charges
When only electric forces act on a charge, its
total mechanical energy, E, will be conserved:
Ei  E f
K i  Ui  K f  U f


23
Example (PP 17.40): Point P is at a potential of 500.0 kV and
point S is at a potential of 200.0 kV. The space between
these points is evacuated. When a charge of +2e moves
from P to S, by how much does its kinetic energy change?
(b) If the particle has a mass of 2.0x10-9 kg and
starts from rest at P, what is its speed at S?
24
Example (text problem 17.41): An electron is accelerated from
rest through a potential difference. If the electron reaches a
speed of 7.26106 m/s, what is the potential difference?
25
Chapter 17: Electric Potential
• Electric Potential Energy
• Electric Potential
• How are the E-field and
Electric Potential related?
• Motion of Point Charges in
an E-field
• Capacitors
• Dielectrics
Free Tutoring & Study
See BlackBoard/C.I.
Practice Exam on BB
For Mon recitation:
• do Online Problems
• do Practice Problems:
• Ch 17 (pp.634-7)
42, 70, 83, 87, 91
Lab: 2.04 (E-field) this week
• Read instructions
• Do Pre-Lab & turn in
• 2.05 (Current) next week
• Exam #1 (Ch 12, 16, 17)
Wed Sep 12, 7:30-8:45pm,
26
095 Overman Hall
§17.5 Capacitors
A capacitor stores electric potential energy by
storing separated (+) and (–) charges.
Work must be done to separate the charges.
+
+
+
+
+
+
+
Parallel plate
capacitor
–
–
–
–
–
–
–
Why?
27
Fig. 17.22
+
+
+
+
+
+
+
V
–
–
–
–
For a parallel plate capacitor:
–
–
–
EQ
E  V
 Q  V
Or
Q = CV
where the proportionality constant C = capacitance
[ Farad = C/V ]
30
What is the capacitance for a parallel plate capacitor?
Q 
V  Ed  (4 k )d  4 k d
A 
 A 
Q  
V  CV
4 kd 
A
where C 
.
4 kd
Note: C is a property of the device,
• it depends on A & d,
• “capacity” to hold charge.
31
Example (PP 17.56): A parallel plate capacitor has a
capacitance of 1.20 nF. There is a charge of magnitude
0.800 mC on each plate.
(a) What is the potential difference between the plates?
(b) If the plate separation is 0.3 mm, what is the area?
(c) If the plate separation is doubled while the charge is kept
constant, what will happen to the potential difference,
and to the potential energy stored in the capacitor?
32
§17.6 Dielectrics
+
+
+
+
+
+
+
–
–
–
–
–
–
–
I. Air-filled capacitor:
Increase Q  increase E
Atoms in air b/w plates gets polarized:
Eventually electrons pulled off (ionized),
Charge arcs across gap = “breakdown”
Need a better insulator!
dielectric strength (kV/mm)
33
+
+
+
+
+
+
+
–
–
–
–
–
–
–
II. Add a dielectric w/
dielectric constant k
Atoms polarize
Charge separation at ends
Reduces E inside dielectric
Can add more Q to plates
Higher C = Q/V
A
C k
 kC0
4kd
34
Example (PP 17.71): A capacitor can be made from two
sheets of aluminum foil separated by a sheet of waxed paper.
If the sheets of aluminum are 0.3 m by 0.4 m and the waxed
paper, of slightly larger dimensions, is of thickness 0.030 mm
and has k = 2.5, (a) what is the capacitance of this capacitor?
(b) How much charge can it hold before breakdown?
(c) How much energy is stored at this point?
36
McGuiver?!
§17.7 Energy Stored in a
Capacitor
A capacitor will store energy equivalent to the amount of
work that it takes to separate the charges.
37
The energy stored in the electric field between the plates is:
1
U  QV
2
1
2
 C V 
2
Q2

2C
}
(Sub in Q = CV)
Summary:
• C is set by the device (A, d, k)
• V is set by the strength of the battery (“pump”)
• Q and U depend on C and V.
38
Example (PP 17.79): A parallel plate capacitor is composed of
two square plates, 10.0 cm on a side, separated by an air gap
of 0.75 mm.
(a) What is the charge on this capacitor when the potential
difference is 150 volts?
(b) What energy is stored in this capacitor?
39
Summary
•Electric Potential Energy
•Electric Potential
•The Relationship Between E and V
•Motion of Point Charges (conservation of energy)
•Parallel Plate Capacitors (capacitance, dielectrics,
energy storage)
40
§16.6 Conductors in Electrostatic Equilibrium
• Conductors are easily polarized: free electrons move
around freely inside the material.
• Any charges placed on a conductor will arrange themselves
in a stable, unmoving distribution: electrostatic equilibrium.
• For a conductor in electrostatic equilibrium:
1) The E-field inside it is zero (no field lines)
2) Any net charge must reside on the surface
3) Just outside the surface, E is perpendicular to the surface
4) Any excess charge will accumulate where the surface is
highly curved (i.e. a sharp point): E is strongest there.
41
Put 16 nC on the following surface:
Q) Where will charges go?
Q) What will the E-field look like?
Lightning rod
42