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Notes on chapter 17 Pg 502-521
I . Electric potential and potential difference
A. Electric potential energy
1. Need a definition to apply conservation of energy
2. Properties are the same as other types of energy
B. Electric potential energy defined
1. We defined electric field as force per unit charge
2. It is useful to define the electric potential as the
potential energy per unit charge
3. Consider parallel plates with a small positive point
charge (q) placed at point b (see diagram)
a. If charge is released, electric force will do work on
particle
b. Kinetic energy increases
c. Potential energy decreases
d. Potential energy will decrease by an amount
equal to the negative of the work done by the
electric force PE - PE0
e. Electric potential energy is transformed into
kinetic energy and the total energy is conserved.
f. + q has a greatest potential energy at b
- q has greatest potential energy at a
g. electric potential can be expressed as the
potential energy per unit charge
4. Electric potential is given the symbol V
5. If a point charge q has electric potential energy
PEE at some point a, the electric potential V at this
point is given as the following.
PE E
V
q
OR
PEE  qV
V = electric potential
PE = potential energy at a
q = point charge
6. The unit of electric potential is given as Joules per
coulomb, and is given a special name , the volt, in
honor of Alessandro Volta
(1745-1827)
7. Another relationship for potential energy.
a. Potential energy is defined as qV and qV is equal
to the work done on the charge.
b. PEE = W
c. Since W = Fd or W= Fr we can derive another
relationship for PE
we start with the following :
PEE  qV
sin ce qV  W
PEE  W
or
PEE  Fd
By substitution we can replace F with the electrostatic
force relationsh ip d is relaced with r
PEE 
kq1q2
r
2
r
or
PEE 
kq1q2
r
Where
PEE = Potential energy
k = electrostatic constant
q1 = first charge
q2 = second charge
r = distance between them
8. Combining the two relationships for potential
energy
kq1q2
PEE  qV 
r
C. Important to note that if finding potential at a point,
that potential depends on where you define zero.
1. zero can be chosen arbitrarily as in mechanical
potential energy
2. usually a ground or a conductor connected to the
ground is taken as a zero potential
a. if you have a point where the potential is 50 V , it
states the potential difference between that point
and the ground is 50V
b. sometimes we could choose the potential to be
zero at infinity
II. Electric field derived for a UNIFORM ELECTRIC
FIELD
A. Look at the work done by the electric field to move a
positive charge q from a to b.
W  qV
Note : work done by the electric field is equal to the negative of the change in
potential energy or
W   qV
Since
F  qE
where E is the uniform electric field
We can say that
W  Fd  qEd
distance
where d is the dis
tan ce between the parallel plates
B. We now have a relationship where
qEd   qV
or by cancelling q from both sides
Ed  V
Since
F  qE
E
V
d
finally we have, for a uniform electric field
E = electric field
(uniform)
V = potential
d = distance
between the
plates
Note: the negative tells
you the direction of the
decreasing potential V
III. Equipotential lines
A. Lines of equal potential within the electric field
B. All points on a line are at the same potential
C. The potential difference between any two points on
the same line is zero
D. No work is done moving a charge from one point to
another on the same equipotential line
E. EQUIPOTENTIAL LINE MUST BE
PERPENDICULAR TO THE ELECTRIC FIELD
1. Since the field lines and equipotential lines are
perpendicular, locating the equipotential lines
are easy when the electric field lines are known
2. Equipotential lines are continuous and never end
unlike electric field lines
F. Conducting surfaces are equipotential surfaces
(could be three dimensions)
G. See diagrams:
IV. Electron volt
A. The joule is a very large unit of energy when
describing energies on the atomic level
B. There is a unit for describing energy when discussing
small numbers Named an electron volt
C. Electron volt defined
1. The electron volt (eV) is defined as the energy
acquired by a particle carrying a charge equal to
that on the electron, (q = e) as a result of moving it
through a potential difference of 1 V.
2. The charge of an electron is 1.6x 10-19 C
3. Since the change in potential energy is equal to qV
we can say the following:
1eV = (1.6x 10-19 C) (1V) = 1.6x 10-19 J
OR
1eV = 1.6x 10-19 J
D. An electron volt that accelerates through a potential
difference of 1000V will lose 1000eV of potential
energy, and will gain 1000eV of kinetic energy. (
Note: if the charge equals twice that of the electron,
2e = 3.2x 10-19 C, when it moves through a potential of
1000 V its energy will change by 2000eV
E. It is important to note that the electron volt is NOT
the proper SI unit, and it must be converted to joules
when calculating energies (potential and kinetic)
V. Electric potential due to point charges
A. The electric potential at a distance r from a single
point charge q can be derived from the expression for
its electric field.
B. Electric potential due to a point charge
V k
q
r
OR
Where
k = electrostatic constant
q = point charge
q q

q
V  k  1  2  3  .... 
 r1 r2 r3

r = distance away from that
point charge
C. Think of V as representing the absolute potential
where V = 0 and r = , or think of V as the potential
difference between r and infinity (see diagram)
1. Note: The potential decreases with the first
power of the distance where the electric field
decreases as the square of the distance.
2. The potential near a positive charge is large and
decreases towards zero at large distances.
3. The potential near a negative charge is negative
and increases towards zero at large distances.
(signs on the charges are important, you must
include them)
VII. Capacitance
A. A Capacitor is device that can temporarily store
electrical charge
B. Sometimes called a condenser
C. Made up of two conducting plates or sheets placed
near each other but not touching
D. Many uses
1. Cameras
2. tasers
3. Cardiac resuscitators
4. Computers, etc.
E. A typical capacitor consists of two parallel plate of
area (A) separated by a small distance d
1. Often two parallel plates are rolled into a cylinder
2. Other times they are left flat
F. Symbol for capacitor is
(see diagram)
G. If voltage is applied to a capacitor by connecting
the capacitor to a battery it quickly becomes charged.
Amount of charge Q acquired is proportional to the
potential difference
Q = CV
Q = charge acquired
V = Potential difference
C = Constant of proportionality or capacitance
of the capacitor
H. Capacitance
1. describes the amount of charge per potential
difference a capacitor has
2. capacitance is measured in farad (f)
3. most capacitors have a capacitance in the range of
1pf (pico farad = 10-12f) to 1f (microfarad = 10-6f)
4. capacitance is a constant
a. does not depend on Q or V
b. its value depends only on the structure and
dimension of the capacitor itself
5. Capacitance is determined by the following factors
a. Area of the plate
b. Distance of separation between the plates
C = capacitance
c.
A = area of plates
A
C  0
d
d = distance of
separation
12 2
2
0 = 8.85  10 C / Nm ( permittivity
of free space)
VIII. Dielectrics
A. An insulating sheet placed between two parallel
plates
B. Serve several purposes
1. higher voltage can be applied without charges
passing across the gap
2. Plates can be placed closer together allowing d to
decrease thus increasing capacitance (see diagram)
C. Capacitance is increased by a factor k which is a
dielectric constant
1. table of dielectric constants pg 514
C = capacitance
2. for a capacitor
A
C  k 0
d
A = area of plates
k = dielectric constant
(depending on material)
12 2
2
0 = 8.85  10 C / Nm ( permittivity
of free space)
IX. Storage of electrical energy
A. Charged capacitor stores electrical energy
B. Energy stored in capacitor is equal to the work done
to charge it
1. battery removes charge from one plate
2. battery adds charge to the other plate.
C. It requires work to add more charge
D. The more charge on the plate the more work is
required to add more charges
1. No work is required if plates are uncharged
2. As more charges are on plate, more work is
required
3. We take an average of the work done where no
work is done at the beginning and a maximum
work is done at the end of a charge. From this idea
we can quantify energy as
U  energy 
1
QV
2
OR
U
U = energy
2
1
1
1Q
2


QV
CV
2
2
2 C
Q = charge
C = capacitance
V = voltage