Download Electric Potential

Electric
Potential
AP Physics: M. Blachly
Textbook: 17:1-3
Review of Work
Work done by the force given by:
• W = F d cos(q)
• Positive: Force is in direction moved
• Negative: Force is opposite direction moved
• Zero: Force is perpendicular to direction moved
TnR
If a positive charge were moved from very far
away on the right to one of the positions shown,
at what position would it have the greatest
amount of stored energy?
+
D
C
B
A
Work on Charges
Work, force,
electric field and
Electrical Energy
are always
considered from
the point of view
of a positive
charge.
Electrostatic Potential Energy and
Potential Difference
The electrostatic force is
conservative – potential
energy can be defined
Change in electric potential
energy is negative of work
done by electric force:
(17-1)
Electrostatic PE and Potential Difference
Electric potential (Voltage) is defined as
potential energy per unit charge:
(17-2a)
TnR
Given the definition of the voltage, what would
be the proper units for Voltage?
A. Joules
B. Joules/Volt
C.Joules/Coulomb
D.Volts/Coulomb
Electrostatic PE and Potential Difference
Electric potential is defined as potential
energy per unit charge:
(17-2a)
Unit of electric potential: the volt (V).
1 V = I J/C.
17.1 Electrostatic Potential Energy
Only changes in potential can be measured,
allowing free assignment of V = 0. (like
solving gravitational PE problems)
(17-2b)
17.1 Electrostatic PE
Analogy between gravitational and electrical
potential energy:
Electric Potential and Electric Field
Work is charge multiplied by potential:
Work is also force multiplied by
distance:
Equi-potential Lines
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.
17.3 Equipotential Lines
The electron
How much potential energy does a single
electron have if it is moved across a potential of
1.0 volts?
U
V
so
q
U  qV
 1.6 10
 1.6 10
19
19
C  1 V 
J
The Electron Volt, a Unit of Energy
One electron volt (eV) is the energy gained by
an electron moving through a potential
difference of one volt.
Potential Due to Point Charges
The electric potential due to a point charge
can be derived using calculus.
(17-5)
 o  8.85 10
12
2
C
2
N×m
Concept Check
A charge of 3.0 nC is placed at the
origin. What is the voltage at a
point that is 30. cm away?
V = 90 V
What about at a point that is a mile
away?
V = 0.017 V
What about a point that is infinitely
far away?
V=0V
Potential Due to Point Charges
These plots show the
potential due to (a)
positive and (b) negative
charge.
Potential Due to Point Charges
Using potentials instead of fields can make
solving problems much easier – potential is a
scalar quantity, whereas the field is a vector.
Example: Old fashioned TV
An electron is accelerated across a potential of
5000 V. What is the velocity of the electron after
passing through this potential difference?
Example: Old fashioned TV
An electron (m = 9.11E-31 kg) is accelerated
across 5000 V. Find the velocity in terms of c.
PE  KE
1 2
qV  mv
2
2qV
v
m
v
2 1.6 10
19
C   5000 J 
 9.1110
31
kg 
v  4.19 10 m/s  0.140c
7
17.7 Capacitance
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.
Capacitance
Charge vs. Voltage for a Capacitor
6
Stored Charge (C)
Q = 0.5 V
5
4
3
2
1
0
0
2
4
6
Voltage (V)
8
10
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)
TnR
What is a Farad?
A. Coulomb/Joule
B. Coulomb/Volt
C.Joule/Coulomb
D.Volt/Coulomb
Answer: B
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:
A
C  o
d
 o  8.85 10
12
2
C
2
N×m
17.8 Dielectrics
A dielectric is an insulator, and is
characterized by a dielectric constant K.
Capacitance of a parallel-plate capacitor filled
with dielectric:
(17-9)
17.8 Dielectrics
Dielectric strength is the
maximum field a
dielectric can experience
without breaking down.
17.8 Dielectrics
The molecules in a dielectric tend to become
oriented in a way that reduces the external
field.
17.8 Dielectrics
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.
TnR
For a capacitor connected to a
battery of fixed voltage, what
will adding a dielectric material
do?
A. Decrease the charge
stored
B. Increase the charge stored
C.It will not affect the amount
of charge stored.
Answer: B
17.9 Storage of Electric Energy
A charged capacitor stores electric energy;
the energy stored is equal to the work done
to charge the capacitor.
2
1
1
1Q
2
U  QV  CV 
2
2
2 C
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!
17.9 Storage of Electric Energy
Heart defibrillators use electric
discharge to “jump-start” the
heart, and can save lives.
Camera’s use a capacitor
discharge to fire the flash
17.10 Cathode Ray Tube
A cathode ray tube
contains a wire cathode
that, when heated, emits
electrons. A voltage
source causes the
electrons to travel to the
anode.
17.10 Cathode Ray Tube
The electrons can be steered using electric
fields.
17.10 Cathode Ray Tube
Televisions and computer monitors (except for
LCD and plasma models) have a large
cathode ray tube
as their display.
Variations in the
field steer the
electrons on their
way to the screen.
17.11 The Electrocardiogram (ECG or EKG)
The electrocardiogram
detects heart defects by
measuring changes in
potential on the surface
of the heart.
Summary of Chapter 17
• Electric potential energy:
• Electric potential difference: work done to
move charge from one point to another
• Relationship between potential difference
and field:
Summary of Chapter 17
• Equipotential: line or surface along which
potential is the same
• Electric potential of a point charge:
Summary of Chapter 17
• Capacitor: nontouching conductors carrying
equal and opposite charge
•Capacitance:
• Capacitance of a parallel-plate capacitor:
Summary of Chapter 17
• A dielectric is an insulator
• Dielectric constant gives ratio of total field to
external field
• Energy density in electric field:
Capacitor Networks
When there are multiple capacitors in series, the
capacitors will all have the same charge.
Qn  Q1  Q2 [1] and Vn  V1  V2 [2]
Since Q  CV , we can rewrite [2] as
Qn Q1 Q2
 
and since Q is all the same,
Cn C1 C2
1
1
1
 
capacitor network in series
Cn C1 C2
Example Problem: Series
What is the equivalent capacitance of a network
consisting of a 9.0 µF capacitor and a 18 µF
capacitor in series? (Answer in µF).
What will be the charge on the smaller capacitor
if this network is connected to a 12 volt battery?
(Answer in µC )
What will be the voltage on the bigger capacitor?
Capacitor Networks
When there are multiple capacitors in parallel, the
capacitors will all have the same voltage.
Vn  V1  V2 [1] and Qn  Q1  Q2 [2]
Since Q  CV , we can rewrite [2] as
VnCn  V1C1  V2C2 and since V is all the same,
Cn  C1  C2 capacitor network in parallel
Example Problem: Parallel
What is the equivalent capacitance of a network
consisting of a 9.0 µF capacitor and a 18 µF
capacitor in parallel? (Answer in µF).
What will be the voltage on the smaller capacitor
if this network is connected to a 12 volt battery?
(Answer in V )
What will be the charge on the smaller capacitor?
(Answer in µC )
Example: Capacitors
Example: Capacitors
Example: Capacitors