Transcript 16ElectEnergycapac

AP Physics
Today’s Agenda
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CHAPTER 16 - ELECTRIC POTENTIAL AND ELECTRIC
ENERGY; CAPACITANCE
Chp 16 problems 1,5,7,9,13,15,17,19
Physics II, Pg 1
OBJECTIVES:After studying
the material of this chapter the
student should be able to:
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1. Write from memory the definitions of electric potential and
electric potential difference.
2. Distinguish between electric potential, electric potential
energy and electric potential difference.
3. Draw the electric field pattern and equipotential line pattern
which exist between charged objects
4. Determine the magnitude of the potential at a point a
known distance from a point charge or an arrangement of
point charges.
5. State the relationship between electric potential and
electric field and determine the potential difference between
two points a fixed distance apart in a region where the electric
field is uniform.
Physics II, Pg 2
OBJECTIVES
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6. Determine the kinetic energy in both joules and electron
volts of a charged particle which is accelerated through a
given potential difference.
7-9 At a later date
7. Explain what is meant by an electric dipole and determine
the magnitude of the electric dipole moment between two
point charges.
8. Given the dimensions, distance between the plates and
the dielectric constant of the material between the plates,
determine the magnitude of the capacitance of a parallel
plate capacitor.
9. Given the capacitance, the dielectric constant and either
the potential difference or the charge stored on the plates of
a parallel plate capacitor, determine the energy and the
energy density stored in the capacitor.
Physics II, Pg 3
KEY TERMS AND PHRASES
 electric potential
electric dipole moment
electric potential difference
debye
electric potential energy
 voltage
 equipotential lines
 electron volt
 electric dipole
capacitor
farad
microfarad
picofarad
energy density
Physics II, Pg 4
ELECTRIC POTENTIAL AND POTENTIAL
DIFFERENCE
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The ELECTRIC
POTENTIAL at point a
(Va) equals the electric
potential energy (PEa)
per unit charge (q)
placed at that point.
V A= PE A /q
Physics II, Pg 5
The ELECTRIC POTENTIAL
DIFFERENCE between two
points (V A) is measured by the
work required to move a unit of
electric charge from point b to
point a.
Vab = Va - Vb = Wab/q
The potential difference
can also be discussed in terms of
the change in potential energy of
a charge q when it is moved
between points a and b.
PE = PEa - PEb= q V., and
therefore Vb= PE/q
Physics II, Pg 6
VOLTAGE
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Potential difference is often referred to
as VOLTAGE.
Both potential and potential difference
are scalar quantities which have
dimensions of Joules/Coulomb.
 The SI unit of electric potential and
potential difference is the VOLT (V),
where I V = I J/C.
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Physics II, Pg 7
Electric Potential and Electric Field
Physics II, Pg 8
Electric Potential and Electric Field
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The effects of any charge distribution can be described in terms of
electric field or in terms of electric potential
The work done by the electric field to move a positive charge is
W=Vba q
The work done by the electric field is also W= Fd where the force
on the positive charge in a uniform electric field is F=qE and d is
the distance (parallel to the field lines) between points a and b.
Physics II, Pg 9
Electric Potential and Electric Field
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W= Fd=q Vba =qEd
Vba = Ed (uniform field)
E= Vba /d (uniform field)
Equivalent units: N/C= Nm/Cm = J/Cm =V/m
Physics II, Pg 10
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If the charged particle is in an electric field which is
uniform, i.e., constant in magnitude and
direction, then the potential difference is related to
the electric field as follows
Vab = E d Cos 
b
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Vab
a
E is the electric field strength in N/C, d is the distance
between points a and b in meters and  is the angle
between the electric field vector and the displacement
vector.
Physics II, Pg 11
If the electric field is non-uniform, i.e., varies in
magnitude and direction between points a and
b, then the electric field strength can only be
properly defined over an incremental distance.
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a
b
b
Physics II, Pg 12
If we consider the x component of the electric field (Ex),
then Ex =- V/  x, where  V is the change in
potential over a very short distance  x. The minus sign
indicates that E points in the direction of decreasing V.
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b
Ex =- V/  x
a
Physics II, Pg 13
EQUIPOTENTIAL LINES
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EQUIPOTENTIAL LINES are
lines along which each point
is at the same potential. On
an equipotential surface,
each point on the surface is
at the same potential. The
equipotential line or surface
is perpendicular to the
direction of the electric field
lines at every point. Thus, if
the electric field pattern is
known, it is possible to
determine the pattern of
equipotential lines or
surfaces,and vice versa.
Physics II, Pg 14
In the following diagrams, the dashed lines
represent equipotential lines and the solid lines the
electric field lines.
Physics II, Pg 15
THE ELECTRON VOLT
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The energy gained by a charged particle which is
accelerated through a potential difference can be
expressed in ELECTRON VOLTS (eV) as well as joules.
Higher amounts of energy can be measured in KeV or
MeV.
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I eV = 1.6 x 10-19 J and I KeV = 103eV and I Mev = 106
eV.
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eV is NOT a proper SI Unit. The joules unit should
really be used when calculating kinetic energy
changes.
Physics II, Pg 16
•ELECTRIC POTENTIAL DUE TO A POINT
CHARGE
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E= kQ/r2 and V= Ed (d can be considered to be the
same as r) therefore V = kQ/r
The electric potential due to a point charge q at a
distance r from the charge is given by
V = kQ/r= (1/4  0 ) Q/r
Note that the zero of potential is arbitrarily taken to be
at infinity ( For a negative charge, the potential at
distance r from the charge is less than zero. As r
increases, the potential increases toward zero,
reaching zero at r)
If more than one point charge is present, the potential
at a particular point is equal to the arithmetic sum of
the potential due to each charge at the point in
question. Sound familiar?
Physics II, Pg 17
ELECTRIC DIPOLE
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Two equal point charges q,
of opposite sign, separated
by a distance are called an
ELECTRIC DIPOLE.
Since V is equal to the sum
of the potentials of the
individual charges:
Physics II, Pg 18
ELECTRIC DIPOLE
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If r >>l the equation can be simplified. (yeah right!)
 r  l cos 
Since r >>  r, it’s contribution to the sum (r +  r) can
be neglected in the denominator
Therefore
Where  is between 0 and 90 degrees,and V is positive.
Where  is between 90 and 180 degrees,and V is
negative
Notice that the V depends on r2
As r gets larger, V gets smaller much faster with a
dipole……… Why?
Physics II, Pg 19
ELECTRIC DIPOLE
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The product Ql is the
DIPOLE MOMENT (p) and
the potential can be
written v = k p cos /r2
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The SI unit of the dipole
moment (p) is the DEBYE,
where I debye = 3.33 x 10
C m.
In polar molecules, such
as water, the molecule is
electrically neutral but
there is a separation of
charge in the molecule.
Such molecules have a
net dipole moment.
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Physics II, Pg 20
CAPACITANCE AND DIELECTRICS
Physics II, Pg 21
CAPACITANCE AND DIELECTRICS
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A CAPACITOR stores electric charge and consists of two
conductors separated by an insulator known as a dielectric.
The ability of a capacitor to store electric charge is referred
to as CAPACITANCE (C) and is found by the following
equation:
C = Q/V
Q is the charge stored in coulombs and V is the potential
difference between the conducting surfaces in volts.
The SI unit of capacitance is the farad (F), where I farad = I
coulomb/volt (1 F = I C/V).
Typical capacitors have values which range from I
picofarad (I pF) to 1 microfarad (1 F) where
I pF = I x 10-12 F and I  F =I x 10-6 F
Physics II, Pg 22
CAPACITANCE AND DIELECTRICS
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The capacitance of a capacitor
depends on the physical
characteristics of the capacitor as
well as the insulating material
which separates the conducting
surfaces which store the electric
charge.
For a parallel plate capacitor, the
capacitance is given by
C = 0 A/d
where 0 is the permittivity of free
space = 8.85 x 1O-12 C2/N m2
Physics II, Pg 23
CAPACITANCE AND DIELECTRICS
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In most capacitors there
is an insulating sheet
(such as paper or plastic)
called a dielectric
between the plates.
Dielectrics break down
less readily than air and
allows plates to be
placed closer together
(without charge passing
across the gap)
For a parallel-plate
capacitor C = K 0 A/d
 = K 0 where  is the
permittivity of the
material.
Physics II, Pg 24
DIELECTRICS
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K is the dielectric constant of the insulating material
between the plates. The constant is
dimensionless and depends on the material. For dry
air at 20'C, the constant is 1.0006. E. is the
permittivity of free space. A is the surface area of one
side of one plate which is opposed by an
the equal area of the other plate and d is the distance
between the plates. E is the permittivity of the
material between the plates.
Physics II, Pg 25