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General Physics II 95.104
Lecture 4
Electric Potential (Ch 17)
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not a substitute for attending lectures.
Topics in Chapter 17
•  Electric Potential Energy
•  Potential Difference (voltage)
•  Equipotential Lines
•  Acceleration of Charged objects by Electric fields
•  The Electron Volt, a Unit of Energy
•  Capacitance
•  Dielectrics
•  Storage of Electric Energy
Electrostatic Potential Energy and
Potential Difference
•  Don’t be intimidated by the names, this is just the work-energy theorem again.
ΔPE=W=F*d.
•  Think about this analogy between gravitational and electrical potential energy:
GPE = mg.h
EPE = qE.d
•  If you push a charge against the electric field, you do work, increasing the object’s EPE.
•  If you release a charge in an E-field, it accelerates, just like dropping a weight. The change in EPE = KE
•  Both Electrostatic and Gravity are inverse square-law forces
•  Both are also Conservative Forces
ConcepTest 17.7a Work and Electric Potential I
1) P → 1
Which requires the most work,
to move a positive charge from
P to points 1, 2, 3 or 4 ? All
points are the same distance
from P.
2) P → 2
3) P → 3
4) P → 4
5) all require the same
amount of work
3
2
1
P
r
E
4
ConcepTest 17.7a Work and Electric Potential I
Which requires the most work,
to move a positive charge from
P to points 1, 2, 3 or 4 ? All
points are the same distance
from P.
For path #1, you have to push the
positive charge against the E field,
which is hard to do. By contrast,
path #4 is the easiest, since the
field does all the work.
1) P → 1
2) P → 2
3) P → 3
4) P → 4
5) all require the same
amount of work
3
2
1
P
r
E
4
Electrostatic Potential Energy and
Potential Difference
The electrostatic force is
conservative
Change in electric potential
energy is negative of work
done by electric force:
Change in PE is the work done either
against (or by) the field, in moving a charge.
Electric Potential
Electric potential is defined as potential
energy per unit charge:
Unit of electric potential: the volt (V).
1 V = I J/C.
(Remember Electric Field was Force per unit charge)
Complete the Conceptual Soundbite:
•  Electric Field (E) is _____ per unit ______
•  Electric Potential (V) is _____ per unit ______
1.  Force, Charge, Energy, Charge
2.  Energy, Charge, Force, Charge
3.  Energy, Force, Force, Mass
4.  Force, Mass, Energy, Mass
Potential Difference
Difference in Potential from one place to
another.
Only changes in potential can be measured,
there is no “absolute zero” for voltage.
Potential difference is work done per unit
charge, so Volts are Joules per Coulomb
17.5 Electric Potential Due to Point
Charges
These plots show the
potential due to (a)
positive and (b) negative
charge.
Physicists often talk
about something “rolling
down a potential” -what
do they mean?
Relation between Electric Potential and
Electric Field
Suppose we want to know the change in potential
energy per unit charge, we call this quantity the
Electric Potential ( symbol “V”)
EPE = W = F.d
= qE.d
(From Newton’s 2nd Law)
Then “Energy per unit charge” would
be V = EPE/q = qEd/q = Ed
Finally note that due to the definition of Electric field and
charge, the potential energy of a positive test charge gets
smaller as the field pushes it from high to low potential, so
we need a minus sign, so:
V = -Ed
Compute the Electric Field between
the two charged wires shown in the
figures below:
7.0 cm
ConcepTest 17.1a Electric Potential Energy I
1) proton
A proton and an electron are in
a constant electric field created
by oppositely charged plates.
You release the proton from the
positive side and the electron
from the negative side. Which
feels the larger electric force?
2) electron
3) both feel the same force
4) neither – there is no force
5) they feel the same magnitude
force but opposite direction
electron
electron
-
+
r
E
proton
proton
ConcepTest 17.1a Electric Potential Energy I
A proton and an electron are in
a constant electric field created
by oppositely charged plates.
You release the proton from the
positive side and the electron
from the negative side. Which
feels the larger electric force?
1) proton
2) electron
3) both feel the same force
4) neither – there is no force
5) they feel the same magnitude
force but opposite direction
Since F = qE and the proton and electron
have the same charge in magnitude, they
both experience the same force. However,
electron
electron
-
the forces point in opposite directions
because the proton and electron are
oppositely charged.
+
r
E
proton
proton
ConcepTest 17.1b Electric Potential Energy II
A proton and an electron are in
a constant electric field created
by oppositely charged plates.
You release the proton from the
positive side and the electron
from the negative side. Which
has the larger acceleration?
1) proton
2) electron
3) both feel the same acceleration
4) neither – there is no acceleration
5) they feel the same magnitude
acceleration but opposite direction
electron
electron
-
+
r
E
proton
proton
ConcepTest 17.1b Electric Potential Energy II
A proton and an electron are in
a constant electric field created
by oppositely charged plates.
You release the proton from the
positive side and the electron
from the negative side. Which
has the larger acceleration?
1) proton
2) electron
3) both feel the same acceleration
4) neither – there is no acceleration
5) they feel the same magnitude
acceleration but opposite direction
Since F = ma and the electron is much less
electron
electron
-
massive than the proton, then the electron
experiences the larger acceleration.
+
r
E
proton
proton
ConcepTest 17.1c Electric Potential Energy III
1) proton
A proton and an electron are in
a constant electric field created
by oppositely charged plates.
You release the proton from the
positive side and the electron
from the negative side. When
it strikes the opposite plate,
which one has more KE?
2) electron
3) both acquire the same KE
4) neither – there is no change of
KE
5) they both acquire the same KE
but with opposite signs
electron
electron
-
+
r
E
proton
proton
ConcepTest 17.1c Electric Potential Energy III
A proton and an electron are in
a constant electric field created
by oppositely charged plates.
You release the proton from the
positive side and the electron
from the negative side. When
it strikes the opposite plate,
which one has more KE?
1) proton
2) electron
3) both acquire the same KE
4) neither – there is no change of
KE
5) they both acquire the same KE
but with opposite signs
Since PE = qV and the proton and electron
have the same charge in magnitude, they
both have the same electric potential energy
initially. Because energy is conserved, they
both must have the same kinetic energy after
they reach the opposite plate.
electron
electron
-
+
r
E
proton
proton
17.3 Equipotential Lines
An equipotential is a line or
surface over which the
potential is constant.
Electric field lines are
perpendicular to
equipotentials.
The surface of a conductor is
an equipotential.
Equipotential Lines
Imagine the green lines are contours on a
map showing a hill and a valley
ConcepTest 17.6 Equipotential of Point Charge
1) A and C
Which two points have
the same potential?
2) B and E
3) B and D
4) C and E
5) no pair
A
C
B
E
Q
D
ConcepTest 17.6 Equipotential of Point Charge
1) A and C
Which two points have
the same potential?
2) B and E
3) B and D
4) C and E
5) no pair
Since the potential of a point charge is:
A
Q
V =k
r
only points that are at the same distance
from charge Q are at the same potential.
This is true for points C and E.
C
B
They lie on an Equipotential Surface.
Follow-up: Which point has the smallest potential?
E
Q
D
ConcepTest 17.7b Work and Electric Potential II
1) P → 1
Which requires zero work, to
move a positive charge from
P to points 1, 2, 3 or 4 ? All
points are the same distance
from P.
2) P → 2
3) P → 3
4) P → 4
5) all require the same
amount of work
3
2
1
P
r
E
4
ConcepTest 17.7b Work and Electric Potential II
Which requires zero work, to
move a positive charge from
P to points 1, 2, 3 or 4 ? All
points are the same distance
from P.
1) P → 1
2) P → 2
3) P → 3
4) P → 4
5) all require the same
amount of work
For path #3, you are moving in a
direction perpendicular to the field
lines. This means you are moving
along an equipotential, which
requires no work (by definition).
Follow-up: Which path requires the least work?
3
2
1
P
r
E
4
The Electron Volt, a Unit of Energy
A charge subjected to an Electric field
experiences a force, and if it is free to move it
accelerates, and hence gains kinetic energy.
(Think of an electron in a TV tube, or X-ray
machine)
One electron volt (eV) is the energy gained by
an electron moving through a potential
difference of one volt.
Cathode Ray Tube: TV and Computer
Monitors, Oscilloscope
Old style Televisions and computer monitors
oscilloscopes etc… have a large
cathode ray tube
as their display.
Variations in the
field steer the
electrons on their
way to the screen.
Imagine an electron accelerated by the electric field
inside a TV tube, how fast does it go ?
+V
Say V = 20,000 volts
Change in EPE = qV = 1.6x10-19 * 20x103
= 3x10-15 Joules
Change in EPE = change in KE = 1/2 mv2
so:
v = sqrt (2KE/m)
= sqrt(2 * 3x10-15 / 9.1x10-31)
= 8.4x107 m/s
In physics we often use eV
because it is a “natural“ unit.
By definition, the electrons
here have a kinetic energy of
20 keV
Capacitance
We have seen that when charges are separated, there is a
force-field between them. This field can both store energy,
and do work.
A capacitor consists of two conductors that are close but
not touching. A capacitor has the ability to store electric
charge.
17.7 Capacitance
Parallel-plate capacitor connected to battery. (b)
is a circuit diagram.
17.7 Capacitance
When a capacitor is connected to a battery, the
charge on its plates is proportional to the
voltage:
(17-7)
The quantity C is called the capacitance.
Unit of capacitance: the farad (F)
1 F = 1 C/V
(or Coulombs per volt)
Think about what the capacitance depends on
ConcepTest 17.8 Capacitors
Capacitor C1 is connected across
1) C1
a battery of 5 V. An identical
2) C2
capacitor C2 is connected across
a battery of 10 V. Which one has
the most charge?
+Q –Q
3) both have the same charge
4) it depends on other factors
ConcepTest 17.8 Capacitors
Capacitor C1 is connected across
1) C1
a battery of 5 V. An identical
2) C2
capacitor C2 is connected across
a battery of 10 V. Which one has
the most charge?
3) both have the same charge
4) it depends on other factors
+Q –Q
Since Q = C V and the two capacitors are
identical, the one that is connected to the
greater voltage has the most charge,
which is C2 in this case.
17.7 Capacitance
The capacitance does not depend on the voltage; it is a function of the
geometry and materials of the capacitor.
For a parallel-plate capacitor:
(17-8)
In other words the Capacitance is fixed, and determines how much charge is
stored for a given applied Voltage.
Capacitance depends on THREE factors
• Area
• Separation (think coulomb force)
• Material
Think about a Capacitor as being like a dam but for electricity
instead of water.
What factors affect the amount of energy that can be stored by
a dam?
A.  Height of the dam
B.  Volume of the lake
C.  Shape of the lake
D.  Area of the lake
ConcepTest 17.9a Varying Capacitance I
What must be done to
1) increase the area of the plates
a capacitor in order to
2) decrease separation between the plates
increase the amount of
3) decrease the area of the plates
charge it can hold (for
a constant voltage)?
4) either (1) or (2)
5) either (2) or (3)
+Q –Q
ConcepTest 17.9a Varying Capacitance I
What must be done to
1) increase the area of the plates
a capacitor in order to
2) decrease separation between the plates
increase the amount of
3) decrease the area of the plates
charge it can hold (for
a constant voltage)?
4) either (1) or (2)
5) either (2) or (3)
+Q –Q
Since Q = C V, in order to increase the charge
that a capacitor can hold at constant voltage,
one has to increase its capacitance. Since the
capacitance is given by C = ε 0
A
, that can be
d
done by either increasing A or decreasing d.
Dielectrics -Improving the basic capacitor
A dielectric is an insulator, placed between the
capacitor’s plates, and is characterized by a
dielectric constant K.
Capacitance of a parallel-plate capacitor filled
with dielectric:
(17-9)
Inserting a dialectric INCREASES the capacitance
Why?
Dielectrics - what’s going on inside a Capacitor?
Dialectrics increase the amount of charge a capacitor can hold, at a given
voltage. The molecules in a dielectric tend to become oriented in a way that
reduces the external field.
This means that the electric field within the dielectric is less than it would be in
air, allowing more charge to be stored for the same potential.
Alternative conceptual viewpoint: The induced charges of the
molecules in the dialectric (an insulator) attract additional charges onto
the plates (from the battery).
17.8 Dielectrics
Dielectric strength is the
maximum external field a
dielectric can experience
without breaking down.
Think about factors
affecting suitability in
different applications
e.g.
Look at water, but its not
usually a good choice!
Say a capacitor is connected to a battery and charged.
We then slide a piece of plastic between the plates.
What happens?
1.  Nothing
2.  More charge flows onto the plates (from the battery)
3.  Some charge flows out of the plates (back to the
battery)
The keys in your computer/laptop
keyboard are all capacitors
Pressing the key squeezes the two charged plates closer
together, changing the capacitance
17.9 Storage of Electric Energy
A Capacitor’s main use is to store energy. It
can be charged slowly and then discharged
rapidly. For example in a camera flash unit.
A charged capacitor stores electric energy;
the energy stored is equal to the work done
to charge the capacitor.
(17-10)
See this week’s HW question about boiling water
17.9 Storage of Electric Energy
The energy density, defined as the energy per
unit volume, is the same no matter the origin of
the electric field:
(17-11)
The sudden discharge of electric energy can be
harmful or fatal. Capacitors can retain their
charge indefinitely even when disconnected
from a voltage source – be careful!
A capacitor consisting of two large metal plates, is
charged, and then disconnected from the battery.
What happens if I pull the plates further apart?
1.  Nothing
2.  Increase the energy stored on the capacitor
3.  Decrease the energy stored in the capacitor
4.  Increase the charge stored
5.  Decrease the charge stored
17.11 The Electrocardiogram (ECG or EKG)
The electrocardiogram
detects heart defects by
measuring changes in
potential on the surface
of the heart.
Summary
•  Electric potential energy:
•  Electric potential difference: work done to
move charge from one point to another
•  Relationship between potential difference
and field:
• Work done by (or against) an Electric Field
W = qV
• Equipotential: line or surface along which
potential is the same
Capacitors
•  Nontouching conductors carrying equal and
opposite charge. Shape irrelevant.
• Capacitance:
unit is the Farad (joule per coulomb)
•  Capacitance of a parallel-plate capacitor:
• Energy stored in a capacitor
Next Lecture: Electric Circuits (Ch 18)
ConcepTest 17.9b Varying Capacitance II
A parallel-plate capacitor
1) the voltage decreases
initially has a voltage of 400 V
2) the voltage increases
and stays connected to the
3) the charge decreases
battery. If the plate spacing is
now doubled, what happens?
4) the charge increases
5) both voltage and charge change
+Q –Q
ConcepTest 17.9b Varying Capacitance II
A parallel-plate capacitor
1) the voltage decreases
initially has a voltage of 400 V
2) the voltage increases
and stays connected to the
3) the charge decreases
battery. If the plate spacing is
now doubled, what happens?
4) the charge increases
5) both voltage and charge change
Since the battery stays connected, the
voltage must remain constant ! Since
C = ε 0 A when the spacing d is doubled,
d
the capacitance C is halved. And since
Q = C V, that means the charge must
decrease.
Follow-up: How do you increase the charge?
+Q –Q
ConcepTest 17.9c Varying Capacitance III
A parallel-plate capacitor initially has
a potential difference of 400 V and is
then disconnected from the charging
battery. If the plate spacing is now
doubled (without changing Q), what
is the new value of the voltage?
+Q –Q
1) 100 V
2) 200 V
3) 400 V
4) 800 V
5) 1600 V
ConcepTest 17.9c Varying Capacitance III
A parallel-plate capacitor initially has
a potential difference of 400 V and is
then disconnected from the charging
battery. If the plate spacing is now
doubled (without changing Q), what
is the new value of the voltage?
Once the battery is disconnected, Q has to
remain constant, since no charge can flow
either to or from the battery.
Since
C = ε 0 A when the spacing d is doubled, the
d
capacitance C is halved. And since Q = C V,
that means the voltage must double.
1) 100 V
2) 200 V
3) 400 V
4) 800 V
5) 1600 V
+Q –Q