Download Chapter 18 - Purdue Physics

PHYS219 Fall semester 2014
Lecture 05: Electrostatic
Potential and Capacitors
Dimitrios Giannios
Purdue University
From electric potential energy
to electric potential
kQqtest
PEE =
r
PEE kQ
V=
=
qtest
r
potential energy
electric potential
PEE
2PE
+
Q
r
2q
qtest
(remember how from FE  E = FE /q)
NEW Concept: The Electric Potential V
The electric potential V at a location in space is the measure
of how much electric potential energy will be generated by
placing a charge +qtest at that location
(
)
Units of Electrostatic Potential:
Electrostatic Potential
=
Electrostatic Potential Energy
Charge
Joules =Volt
=
Coulomb
The Electric Potential V for a Point
Charge q
q
For a system of point charges, what is the
electrostatic potential V at point A?
+q
test
Note:
i) Here, q1 , q2 , etc. are SIGNED quantities
ii) The potential V does NOT depend on qtest
Example:
What is the electrostatic potential at point P?
Note: 1 pC=1 x 10-12 C; 1 μm = 1 x10-6 m
q4=5.0 pC
q5=-15.0 pC
r5= 4.0 μm
r4= 5.0 μm
P
X
r1= 8.0 μm
r3= 3.5 μm
q1=10.0 pC
r2= 4.7 μm
q3=-8.0 pC
q2=25.0 pC
5
Visualizing the Electric Potential
Equipotential Surfaces
Gravitational
Equipotentials: contour
lines on a topographic map
Can be measured with an
altimeter!
Electrostatic
Equipotentials
Can be measured with an
electrostatic voltmeter!
The potentially damaging potential
Example: The electric
potential difference between
a storm cloud and earth is
100 million volts. If 2 C of
charge is dumped from the
cloud into earth, what is the
change in potential energy of
the charge?
2C
ΔV = 100 x 106 V
Example: A point charge of +25 μC is moved from
Point A to Point B. How much work is required?
A
x qtest
Path I
Path II
Path III
x B
60 V
50 V
40 V
30 V
You can show that
10 V
20 V
From concepts to real life
The discussion today may seem abstract, but
it lays the groundwork for analyzing
electrical circuits.
A qtest
B
Δ(PE E ) = q test Δ V
Note
If you understand this material, you
should be able to distinguish between
two closely related concepts
Electrostatic Potential Energy (J)
vs.
Electrostatic Potential (V)
The electrostatic potential can be high, but
the electrostatic potential energy can be quite
low IF a small amount of charge is involved.
The energy transferred when charging or
discharging is related to changes in the
electrostatic potential energy.
Capacitors
How Can You Store a Lot of Charge?
Capacitors store charge and so store energy
Parallel Plate Capacitor
Charging up a Capacitor
EXPERIMENT
V
Voltage
across
Plates
δQ
How much work do I have to
do to move the charge δQ?
work done by electric forces:
W = -Δ(PEE) = -V(δQ)
δV
Charge
Q
Transferred
What happens to
my effort?
Capacitance C of capacitor:
ability to store charge
The capacitance C of a capacitor tells
about its ability to store charge
from experiment:
q∝ ΔV
q = C ΔV
NOTE: Each plate
has the same amount
of charge: positive on
one plate and
negative on the
other. The total
charge is zero.
Capacitance is a very general
concept. It applies to any two
objects, even if they are not
parallel plates.
Units of capacitance C is Coulomb/Volt = [Farad] or [F]
Example: Understanding the definition
of capacitance
The standard, simple model for a
parallel plate capacitor
E inside is uniform
to a good
approximation.
-12
E outside is zero to a
good approximation
parallel plate capacitor filled with air
Note 1: εo=8.85×10-12 C2/(N•m2)
Note 2: C depends on geometry
Note 3: A is area of one plate
What is the Capacitance?
=1
=1 mm
=1 cm
cm
air-filled