Download 16.1 Electric Potential Energy and Electric

Lecture Outline
Chapter 16
College Physics, 7th Edition
Wilson / Buffa / Lou
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The Why??
• X-rays
• Heart Defibrillators
• Nervous System
16.1 Electric Potential Energy and
Electric Potential Difference
• The simplest electric field pattern is between
2 large, oppositely charged plates. (How do
we calculate electric field?)
• Let’s talk about each picture…
• Work Formula is…
16.1 Electric Potential Energy and
Electric Potential Difference
It takes work to move a charge against an
electric field. Just as with gravity, this work
increases the potential energy of the charge.
To find the change in potential energy you use
the formula below:
Why is this the same equation as Work?
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16.1 Electric Potential Energy and
Electric Potential Difference
Just as with the electric field, it is convenient
to define a quantity that is the electric
potential energy per unit charge. This is called
the electric potential difference.
Unit of electric potential difference: the volt, V
Which is the same thing as J/C
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16.1 Electric Potential Energy and
Electric Potential Difference
The potential difference between parallel
plates can be calculated relatively easily:
For a pair of oppositely charged parallel plates,
the positively charged plate is at a higher electric
potential than the negatively charged one by an
amount ΔV.
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16.1 Electric Potential Energy and
Electric Potential Difference
• Imagine a moving proton from a negative to positive
plate. The plates are 1.5 cm apart and the field is 1500
N/C.
– a.) What is the change in electric potential energy?
– b.) What is the electric potential difference
– c.) If the proton is released from rest at the positive plate, what
speed will it have just before it hits negative plate?
16.1 Electric Potential Energy and
Electric Potential Difference
Potential differences are defined in terms of
positive charges, as is the electric field.
Therefore, we must account for the difference
between positive and negative charges.
Positive charges, when released, accelerate toward
regions of lower electric potential.
Negative charges, when released, accelerate toward
regions of higher electric potential.
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16.1 Electric Potential Energy and
Electric Potential Difference
• Modern dental offices use Xray machines for diagnosing
different problems. To do this,
electrons are accelerated
through electric potential
differences (voltage) of 25,000
V. When the electrons hit the
positive plates, the kinetic
energy is converted into a
photon. Suppose a single
electron’s kinetic energy is
distributed equally among 5
photons. How much energy
would one photon have?
16.1 Electric Potential Energy and
Electric Potential Difference
In non-uniform
fields, the field
strength can vary.
This diagram shows
the electric potential
difference of a point
charge.
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16.1 Electric Potential Energy and
Electric Potential Difference
Whether the electric potential increases or
decreases when towards or away from a point
charge depends on the sign of the charge.
Electric potential increases when moving nearer to
positive charges or farther from negative charges.
Electric potential decreases when moving farther from
positive charges or nearer to negative charges.
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16.1 Electric Potential Energy and
Electric Potential Difference
• The electric potential at a distance from a
point charge can be calculated using the
following formula:
• V = kq
r
Where k = 9.0 x 109 N m2/C2
16.1 Electric Potential Energy and
Electric Potential Difference
• According to the Bohr Model of the hydrogen atom, the
smallest orbit has a radius of 0.0529 nm, and the next
largest radius has a radius of 0.212 nm.
• a.) How do the values of the electric potentials at each
orbit compare:
– 1.) the smaller orbit is at a higher potential
– 2.) the larger is at a higher potential
– 3.) they have the same potential
• b.) Verify your answer by calculating the electric
potentials.
16.1 Electric Potential Energy and
Electric Potential Difference
The electric potential energy of a system of
two charges is the change in electric potential
multiplied by the charge.
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16.1 Electric Potential Energy and
Electric Potential Difference
The additional potential
energy due to a third
charge is the sum of its
potential energies.
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16.1 Electric Potential Energy and
Electric Potential Difference
• Water is a permanent
polar molecule. The
distance from each H
atom to the O atom is
9.60 x 10-11m, and
the angle between the
two H-O bonds is 104
degrees. What is the
total electrostatic
energy of the water
molecule.
16.2 Equipotential Surfaces and the
Electric Field
An equipotential surface is
one on which the electric
potential does not vary. This
means the potential is the
same.
If the charge is moved
perpendicular to the electric
field, then it takes no work to
move a charge along an
equipotential surface.
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Why would there be no work?
16.2 Equipotential Surfaces and the
Electric Field
Equipotentials are
analogous to
contour lines on a
topographic map.
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16.2 Equipotential Surfaces and the
Electric Field
Equipotentials are
always perpendicular
to electric field lines.
This enables you to
draw one if you know
the other.
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16.2 Equipotential Surfaces and the
Electric Field
Here, these
principles have
been used to draw
the electric field
lines and
equipotentials of an
electric dipole.
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16.2 Equipotential Surfaces and the
Electric Field
The potential difference between any 2 equipotential
planes is found by:
ΔV = EΔx
The direction of the electric field E is that in which the
electric potential decreases the most rapidly. [Draw a pic]
Its magnitude at maximum rate is given by:
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16.2 Equipotential Surfaces and the
Electric Field
• Under normal atmospheric conditions, the Earth’s surface is
electrically charged. This creates an approximately constant
electric field of about 150 V/m pointing down near the
surface.
• a.) Under these conditions, what is the shape of the
equipotential surfaces, and in what direction does the electric
potential decrease most rapidly?
• b.) How far apart are two equipotential surfaces that have a
1000V difference between them? Which has a higher
potential, the one farther from Earth or closer?
16.2 Equipotential Surfaces and the
Electric Field
A solid conductor with an excess
positive charge is shown to the
left. Which of the following best
describes the shape of the
equipotential surfaces just
outside the conductor’s surface:
a.) Flat planes
b.) Spheres
c.) The shape of the conductor’s
surface
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16.2 Equipotential Surfaces and the
Electric Field
The electron-volt (eV) is the amount of energy
needed to move an electron through a potential
difference (voltage) of one volt.
The electron-volt is a unit of energy, not
voltage, and is not an SI standard unit. It is,
however, quite useful when dealing with
energies on the atomic scale.
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16.3 Capacitance
A pair of parallel plates will store electric energy if
charged; this arrangement is called a capacitor. This
energy storage occurs because it takes work to
transfer charge between the plates.
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16.3 Capacitance
• A battery does the work of removing electrons electrons
from the positive plate and transfer (or pump) them
through a wire to the negative plate.
• As a result: a separation of charge occurs and an electric
field will be created.
• The battery will continue to charge the capacitor until the
voltage between the plates is the same as the battery.
– When disconnected from the battery, the capacitor
becomes a storage reservoir of electric energy.
16.3 Capacitance
The charge is related to the potential
difference. Capacitance represents the amount
of charge stored per volt.
SI unit of capacitance: the farad, F
Larger capacitance = more energy/charge
stored.
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16.3 Capacitance
For a parallel-plate capacitor,
C = εo A
d
The quantity inside the parentheses is
called the permittivity of free space, and is
represented by ε0.
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16.3 Capacitance
• What would be the plate area of an air
filled 1.0 F parallel plate capacitor if the
plate separation were 1.0 mm?
16.3 Capacitance
The energy stored in a capacitor is equal to the
work done by the battery. This energy can be
found 3 different ways. 
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16.3 Capacitance
• During a heart attack, the heart can beat in an erratic
fashion, called fibrillation. One way to get it back to
normal rhythm is to shock it with electrical energy
supplied by a cardiac defibrillator. About 300J of energy
is required to produce the desired effect. Typically a
defibrillator stores this energy in a capacitor charged by
a 5000V power supply.
• a.) What capacitance is required?
• b.) What is the charge on the capacitor’s plates?
SKIPPING YO!
• Skipping Dielectrics because will not be
tested on AP Exam.
• This is all of Section 16.4
• 
16.5 Capacitors in Series and in Parallel
• Capacitors can be connected in two basic
ways:
– Series: capacitors are connected head to tail.
– Parallel: all the leads on one side of the
capacitors have a common connection. (all
heads together, or all tails together)
– Let’s look at each of these separately.
16.5 Capacitors in Series and in Parallel
Let’s draw capacitors in a series configuration.
Capacitors in series all have the same charge.
Q1 = Q2 = Q3
The total potential difference is the sum of the
potentials across each capacitor.
Vtotal = V1 + V2 + V3
The total voltage would be the same as the
source of the voltage. So for example…
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16.5 Capacitors in Series and in Parallel
• The equivalent series capacitance (Cs) is defined as the
value of a single capacitor that could replace the series
combination and store the same charge and energy at
the same voltage.
• What the what? Let’s draw a picture.
• Cs is always the smallest capacitance in the series. The smallest
capacitance in a series receives the largest voltage.
16.5 Capacitors in Series and in Parallel
Let’s draw capacitors in a parallel configuration.
Capacitors in parallel all have the same potential
difference (same voltage).
V1 = V2 = V3
The total charge is the sum of the charge on each.
Qtotal = Q1 + Q2 + Q3
The capacitance (Cp) is found by:
Cp is larger than the largest capacitance.
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16.5 Capacitors in Series and in Parallel
We can picture capacitors in parallel as
forming one capacitor with a larger area:
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16.5 Capacitors in Series and in Parallel
• Given two capacitors, one with a capacitance of
2.50 μF, and the other with that of 5.00 μF, what
are the charges on each and the total charge
stored if they are connected across a 12.0 V
battery
– a.) in series
– b.) in parallel
16.5 Capacitors in Series and in Parallel
• 3 capacitors are connected in a
circuit shown to the right.
– a.) By looking at the capacitance
values, how do the voltages across
the capacitors compare?
• V3 > V2 > V1
• V3 < V2 = V1
• V3 = V2 = V1
• V3 = V2 > V1
– b.) Determine the voltages across
each capacitor.
– c.) Determine the stored energy in
each capacitor.
This is considered
a difficult