The document summarizes key concepts from a physics lecture on electric potential including:
1. The electric potential (V) at a point is defined as the work (W) done per unit charge to move a test charge from infinity to that point without acceleration.
2. Equipotential surfaces connect all points of equal electric potential. Electric field lines are always perpendicular to equipotential surfaces.
3. Expressions are derived for the electric potential due to point charges, lines of charge, surfaces of charge, and volumes of charge using integration.
The document discusses the relationship between electric potential, potential energy, and electric fields. It provides background on how electric potential is analogous to gravitational potential and depends on location within an electric field. Examples are given to illustrate how to calculate electric potential, potential differences, and potential energy at different points based on distances from charges.
The document discusses several topics in electrostatics including electric potential, potential difference, equipotential surfaces, Gauss's law, and applications of Gauss's law. Gauss's law states that the electric flux through any closed surface is equal to the enclosed charge divided by the permittivity of free space. This relationship can be used to derive Coulomb's law and calculate electric fields due to various charge distributions like line charges, plane sheets of charge, and spherical shells.
1. The document discusses concepts in electrostatics including the line integral of electric field, electric potential, Gauss's theorem, and applications.
2. Gauss's theorem states that the electric flux through any closed surface is equal to the net charge enclosed divided by the permittivity of free space.
3. The theorem can be used to derive Coulomb's law and calculate electric field intensities due to various charge distributions like line charges and spherical shells.
1. The document discusses various topics in electrostatics including line integrals of electric fields, electric potential and potential differences, Gauss's theorem, and applications of Gauss's theorem.
2. Key concepts covered are the definitions of electric potential and potential difference, the relationship between electric field and potential via line integrals, and Gauss's theorem that the electric flux through any closed surface is equal to the enclosed charge divided by the permittivity of free space.
3. Examples are given of using Gauss's theorem to calculate electric fields, such as for an infinite line charge, planar sheet of charge, and spherical shell of charge.
The document describes concepts from a lecture on electric fields, including:
1. The electric field E at a point is defined as the electric force F on a test charge divided by the charge q. Field lines depict the direction and strength of the field.
2. The electric field due to a point charge is directed away from a positive charge and toward a negative charge.
3. The field of a dipole is non-uniform, exerting a torque and giving the dipole a potential energy depending on its orientation in the field.
4. Continuous charge distributions are treated by summing the contributions of small charge elements to the electric field.
The document describes concepts from a lecture on electric fields, including:
1. The electric field E at a point is defined as the electric force F on a test charge divided by the test charge q. Field lines depict the direction and strength of the electric field.
2. The electric field due to a point charge is directed away from a positive charge and toward a negative charge.
3. The field due to a dipole can be determined by treating it as two point charges. A dipole experiences a torque and potential energy in an external electric field based on its orientation.
The document discusses electrostatics and provides information about an introductory physics course. It defines key concepts like Coulomb's law, electric fields, electric flux, and more. It gives examples and problems to illustrate these concepts. The instructor is Dr. Sabar Hutagalung and the main textbook is Physics for Scientists and Engineers by Serway and Jewett. The document outlines topics to be covered including charge, Coulomb's law, electric fields, Gauss's law, electric potential, and capacitors.
The document discusses the relationship between electric potential, potential energy, and electric fields. It provides background on how electric potential is analogous to gravitational potential and depends on location within an electric field. Examples are given to illustrate how to calculate electric potential, potential differences, and potential energy at different points based on distances from charges.
The document discusses several topics in electrostatics including electric potential, potential difference, equipotential surfaces, Gauss's law, and applications of Gauss's law. Gauss's law states that the electric flux through any closed surface is equal to the enclosed charge divided by the permittivity of free space. This relationship can be used to derive Coulomb's law and calculate electric fields due to various charge distributions like line charges, plane sheets of charge, and spherical shells.
1. The document discusses concepts in electrostatics including the line integral of electric field, electric potential, Gauss's theorem, and applications.
2. Gauss's theorem states that the electric flux through any closed surface is equal to the net charge enclosed divided by the permittivity of free space.
3. The theorem can be used to derive Coulomb's law and calculate electric field intensities due to various charge distributions like line charges and spherical shells.
1. The document discusses various topics in electrostatics including line integrals of electric fields, electric potential and potential differences, Gauss's theorem, and applications of Gauss's theorem.
2. Key concepts covered are the definitions of electric potential and potential difference, the relationship between electric field and potential via line integrals, and Gauss's theorem that the electric flux through any closed surface is equal to the enclosed charge divided by the permittivity of free space.
3. Examples are given of using Gauss's theorem to calculate electric fields, such as for an infinite line charge, planar sheet of charge, and spherical shell of charge.
The document describes concepts from a lecture on electric fields, including:
1. The electric field E at a point is defined as the electric force F on a test charge divided by the charge q. Field lines depict the direction and strength of the field.
2. The electric field due to a point charge is directed away from a positive charge and toward a negative charge.
3. The field of a dipole is non-uniform, exerting a torque and giving the dipole a potential energy depending on its orientation in the field.
4. Continuous charge distributions are treated by summing the contributions of small charge elements to the electric field.
The document describes concepts from a lecture on electric fields, including:
1. The electric field E at a point is defined as the electric force F on a test charge divided by the test charge q. Field lines depict the direction and strength of the electric field.
2. The electric field due to a point charge is directed away from a positive charge and toward a negative charge.
3. The field due to a dipole can be determined by treating it as two point charges. A dipole experiences a torque and potential energy in an external electric field based on its orientation.
The document discusses electrostatics and provides information about an introductory physics course. It defines key concepts like Coulomb's law, electric fields, electric flux, and more. It gives examples and problems to illustrate these concepts. The instructor is Dr. Sabar Hutagalung and the main textbook is Physics for Scientists and Engineers by Serway and Jewett. The document outlines topics to be covered including charge, Coulomb's law, electric fields, Gauss's law, electric potential, and capacitors.
1. The document summarizes key concepts from chapter two on electrostatic potential and capacitance, including the definition of electric potential as the work required to move a test charge between two points in an electric field.
2. It describes how the electric potential depends on the positions of point charges and how to calculate the potential for various charge configurations like a single point charge, dipole, or group of charges.
3. The document also discusses equipotential surfaces and their properties, including that electric field lines are perpendicular to equipotential surfaces and that potential energy can be calculated for systems of charges.
This document discusses the concepts of electric fields and electric field intensity. It defines electric field as a region of space around charged particles that exert electrostatic forces on other charges. Electric field intensity is defined as the electrostatic force per unit positive test charge. The electric field due to a point charge is discussed, along with the superposition principle and electric field lines. Electric dipoles are introduced as pairs of equal and opposite charges, with discussions of dipole fields, dipole moments, and the torque and work done on an electric dipole in a uniform electric field.
JEE Main Advanced 12 Sample ebook, which helps you to understand the chapter in easy way also download sample papers and previous year papers and practice to solve the question on time. Download at www.misostudy.com.
JEE Main 12 Sample ebook, which helps you to understand the chapter in easy way also downaload sample papers and previous year papers and practice to solve the question on time. Download at www.misostudy.com.
This document discusses the concepts of electric fields and electric field intensity. It defines electric field as a region of space around charged particles that exert electrostatic forces on other charges. Electric field intensity is defined as the electrostatic force per unit positive test charge. The electric field due to a point charge is discussed, along with the superposition principle and electric field lines. Electric dipoles are introduced as pairs of equal and opposite charges, with discussions of dipole moment, and the electric field intensity and torque experienced by a dipole in a uniform electric field.
This document discusses the concepts of electric fields and electric field intensity. It defines electric field as a region of space around charged particles that exert electrostatic forces on other charges. Electric field intensity is defined as the electrostatic force per unit positive test charge. The electric field due to a point charge is discussed, along with the superposition principle and electric field lines. Electric dipoles are introduced as pairs of equal and opposite charges, with discussions of dipole moment, and the electric field intensity and torque experienced by dipoles.
*Animated PPT FOR SCHOOL/ Coachings *
Physics , Chemistry , maths , biology
(Improve your teaching style )
*CONTENT*:-
1. ANIMATED THEORY
(COMES ON PRESS KEY ONE BY ONE )
2.MCQ
3. LIVE EXAMPLE
4. ANIMATED IMAGES LIKE
SPRING , CAR ETC
5. ANIMATED
6. CHAPTER WISE QUESTIONS AND SOLUTION WITH ANIMATED IMAGES
7. SEPARATE TOPIC SEPARATE FILES
Live example watch this video
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https://drive.google.com/folderview?id=1KsUPQfeqPQXQ6y6MzoMl07C89yRYhnQt
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No any file miss .
* Work with in zoom ,Google neet , *
contact/whatsapp:- 9753223223
This document discusses the concepts of electric fields and electric field intensity. It defines electric field as a region of space around charged particles that exert electrostatic forces on other charges. Electric field intensity is defined as the electrostatic force per unit positive test charge. The electric field due to a point charge is discussed, along with the superposition principle and electric field lines. Electric dipoles are introduced as pairs of equal and opposite charges, with discussions of dipole moment, and the electric field intensity and torque experienced by dipoles.
Class 12th Physics Electrostatics part 2Arpit Meena
This document discusses the concepts of electrostatics including electric field, electric field intensity, and electric field lines. It defines electric field as a region around charged particles where other charges will experience a force. Electric field intensity is the force per unit charge on a small test charge. The electric field due to a point charge is defined by the equation E=kq/r^2 and has spherical symmetry. The superposition principle states that the total electric field is the vector sum of the fields due to individual charges. Electric field lines are imaginary lines showing the direction of the electric field. Key properties of electric field lines are also discussed. The document further explains the electric field due to an electric dipole, and the torque and work
The document contains information about an upcoming mid-semester physics test, including the date, time, and location. It also provides checkpoint questions from previous lectures on topics like electric charge distribution and electric potential. Finally, it summarizes key concepts relating to electric potential, including definitions, calculations of potential for single and multiple point charges, and the relationship between potential and electric field.
The document contains information about an upcoming mid-semester physics test, including the date, time, and location. It also provides checkpoint questions from previous lectures on topics like electric charge distribution and electric potential. Finally, it summarizes key concepts relating to electric potential, including definitions, calculations of potential for single and multiple point charges, and the relationship between potential and electric field.
This document discusses the concepts of electrostatics including electric field, electric field intensity, and electric field lines. It defines electric field as a region around charged particles where other charges will experience a force. Electric field intensity is the force per unit charge on a test charge in an electric field. An electric field is represented by electric field lines which do not physically exist but show the direction of the field. The document also examines the electric field and field lines due to various charge configurations including point charges, dipoles, and uniform fields. It defines an electric dipole moment and derives expressions for the electric field of a dipole. Finally, it discusses the torque and potential energy of an electric dipole placed in a uniform electric field.
This document discusses the concepts of electrostatics including electric field, electric field intensity, and electric field lines. It defines electric field as a region around charged particles where other charges will experience a force. Electric field intensity is the force per unit charge on a test charge in an electric field. An electric field is represented by electric field lines which emanate from positive charges and terminate at negative charges. The properties and types of electric field lines for different charge configurations such as point charges, dipoles, and uniform fields are described. The document also covers the electric field and torque experienced by an electric dipole when placed in a uniform electric field.
This document discusses the concepts of electrostatics including electric field, electric field intensity, electric field due to point charges, the superposition principle, electric lines of force, properties of electric lines of force, electric dipoles, electric field intensity due to dipoles, torque on dipoles, and work done on dipoles. It defines key terms and concepts and provides examples and equations to illustrate electric field and force calculations for various charge configurations including point charges and dipoles.
The document discusses electric fields and electrostatics. It explains that when objects are rubbed together, electrons are transferred causing objects to become charged. It then discusses Coulomb's law which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. It provides equations for calculating electric field strength, potential, and force experienced by charges in fields.
1. The document discusses electric fields created by point charges and electric dipoles. It defines electric field strength and describes how electric field strength is calculated for point charges and dipoles.
2. Key properties of electric field lines are outlined, including that they emanate from positive charges and terminate at negative charges.
3. Formulas are given for calculating the torque and work done on an electric dipole placed in a uniform electric field. The dipole will experience a torque causing it to rotate into alignment with the field.
The document discusses electric field, potential, and energy. It defines electric potential as the work done to move a unit positive charge from infinity to a point in an electric field. Electric potential is a scalar quantity measured in volts. Equipotentials are regions in space where the electric potential has a constant value, forming equipotential surfaces or lines. Analogies are drawn between electric and gravitational fields, such as both following inverse square laws and having field lines and equipotentials.
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...EduSkills OECD
Andreas Schleicher, Director of Education and Skills at the OECD presents at the launch of PISA 2022 Volume III - Creative Minds, Creative Schools on 18 June 2024.
Temple of Asclepius in Thrace. Excavation resultsKrassimira Luka
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
1. The document summarizes key concepts from chapter two on electrostatic potential and capacitance, including the definition of electric potential as the work required to move a test charge between two points in an electric field.
2. It describes how the electric potential depends on the positions of point charges and how to calculate the potential for various charge configurations like a single point charge, dipole, or group of charges.
3. The document also discusses equipotential surfaces and their properties, including that electric field lines are perpendicular to equipotential surfaces and that potential energy can be calculated for systems of charges.
This document discusses the concepts of electric fields and electric field intensity. It defines electric field as a region of space around charged particles that exert electrostatic forces on other charges. Electric field intensity is defined as the electrostatic force per unit positive test charge. The electric field due to a point charge is discussed, along with the superposition principle and electric field lines. Electric dipoles are introduced as pairs of equal and opposite charges, with discussions of dipole fields, dipole moments, and the torque and work done on an electric dipole in a uniform electric field.
JEE Main Advanced 12 Sample ebook, which helps you to understand the chapter in easy way also download sample papers and previous year papers and practice to solve the question on time. Download at www.misostudy.com.
JEE Main 12 Sample ebook, which helps you to understand the chapter in easy way also downaload sample papers and previous year papers and practice to solve the question on time. Download at www.misostudy.com.
This document discusses the concepts of electric fields and electric field intensity. It defines electric field as a region of space around charged particles that exert electrostatic forces on other charges. Electric field intensity is defined as the electrostatic force per unit positive test charge. The electric field due to a point charge is discussed, along with the superposition principle and electric field lines. Electric dipoles are introduced as pairs of equal and opposite charges, with discussions of dipole moment, and the electric field intensity and torque experienced by a dipole in a uniform electric field.
This document discusses the concepts of electric fields and electric field intensity. It defines electric field as a region of space around charged particles that exert electrostatic forces on other charges. Electric field intensity is defined as the electrostatic force per unit positive test charge. The electric field due to a point charge is discussed, along with the superposition principle and electric field lines. Electric dipoles are introduced as pairs of equal and opposite charges, with discussions of dipole moment, and the electric field intensity and torque experienced by dipoles.
*Animated PPT FOR SCHOOL/ Coachings *
Physics , Chemistry , maths , biology
(Improve your teaching style )
*CONTENT*:-
1. ANIMATED THEORY
(COMES ON PRESS KEY ONE BY ONE )
2.MCQ
3. LIVE EXAMPLE
4. ANIMATED IMAGES LIKE
SPRING , CAR ETC
5. ANIMATED
6. CHAPTER WISE QUESTIONS AND SOLUTION WITH ANIMATED IMAGES
7. SEPARATE TOPIC SEPARATE FILES
Live example watch this video
https://youtu.be/PG4LTFUKi1A
https://drive.google.com/folderview?id=1KsUPQfeqPQXQ6y6MzoMl07C89yRYhnQt
*Delivery in 1 min in Google drive*
No any file miss .
* Work with in zoom ,Google neet , *
contact/whatsapp:- 9753223223
This document discusses the concepts of electric fields and electric field intensity. It defines electric field as a region of space around charged particles that exert electrostatic forces on other charges. Electric field intensity is defined as the electrostatic force per unit positive test charge. The electric field due to a point charge is discussed, along with the superposition principle and electric field lines. Electric dipoles are introduced as pairs of equal and opposite charges, with discussions of dipole moment, and the electric field intensity and torque experienced by dipoles.
Class 12th Physics Electrostatics part 2Arpit Meena
This document discusses the concepts of electrostatics including electric field, electric field intensity, and electric field lines. It defines electric field as a region around charged particles where other charges will experience a force. Electric field intensity is the force per unit charge on a small test charge. The electric field due to a point charge is defined by the equation E=kq/r^2 and has spherical symmetry. The superposition principle states that the total electric field is the vector sum of the fields due to individual charges. Electric field lines are imaginary lines showing the direction of the electric field. Key properties of electric field lines are also discussed. The document further explains the electric field due to an electric dipole, and the torque and work
The document contains information about an upcoming mid-semester physics test, including the date, time, and location. It also provides checkpoint questions from previous lectures on topics like electric charge distribution and electric potential. Finally, it summarizes key concepts relating to electric potential, including definitions, calculations of potential for single and multiple point charges, and the relationship between potential and electric field.
The document contains information about an upcoming mid-semester physics test, including the date, time, and location. It also provides checkpoint questions from previous lectures on topics like electric charge distribution and electric potential. Finally, it summarizes key concepts relating to electric potential, including definitions, calculations of potential for single and multiple point charges, and the relationship between potential and electric field.
This document discusses the concepts of electrostatics including electric field, electric field intensity, and electric field lines. It defines electric field as a region around charged particles where other charges will experience a force. Electric field intensity is the force per unit charge on a test charge in an electric field. An electric field is represented by electric field lines which do not physically exist but show the direction of the field. The document also examines the electric field and field lines due to various charge configurations including point charges, dipoles, and uniform fields. It defines an electric dipole moment and derives expressions for the electric field of a dipole. Finally, it discusses the torque and potential energy of an electric dipole placed in a uniform electric field.
This document discusses the concepts of electrostatics including electric field, electric field intensity, and electric field lines. It defines electric field as a region around charged particles where other charges will experience a force. Electric field intensity is the force per unit charge on a test charge in an electric field. An electric field is represented by electric field lines which emanate from positive charges and terminate at negative charges. The properties and types of electric field lines for different charge configurations such as point charges, dipoles, and uniform fields are described. The document also covers the electric field and torque experienced by an electric dipole when placed in a uniform electric field.
This document discusses the concepts of electrostatics including electric field, electric field intensity, electric field due to point charges, the superposition principle, electric lines of force, properties of electric lines of force, electric dipoles, electric field intensity due to dipoles, torque on dipoles, and work done on dipoles. It defines key terms and concepts and provides examples and equations to illustrate electric field and force calculations for various charge configurations including point charges and dipoles.
The document discusses electric fields and electrostatics. It explains that when objects are rubbed together, electrons are transferred causing objects to become charged. It then discusses Coulomb's law which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. It provides equations for calculating electric field strength, potential, and force experienced by charges in fields.
1. The document discusses electric fields created by point charges and electric dipoles. It defines electric field strength and describes how electric field strength is calculated for point charges and dipoles.
2. Key properties of electric field lines are outlined, including that they emanate from positive charges and terminate at negative charges.
3. Formulas are given for calculating the torque and work done on an electric dipole placed in a uniform electric field. The dipole will experience a torque causing it to rotate into alignment with the field.
The document discusses electric field, potential, and energy. It defines electric potential as the work done to move a unit positive charge from infinity to a point in an electric field. Electric potential is a scalar quantity measured in volts. Equipotentials are regions in space where the electric potential has a constant value, forming equipotential surfaces or lines. Analogies are drawn between electric and gravitational fields, such as both following inverse square laws and having field lines and equipotentials.
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...EduSkills OECD
Andreas Schleicher, Director of Education and Skills at the OECD presents at the launch of PISA 2022 Volume III - Creative Minds, Creative Schools on 18 June 2024.
Temple of Asclepius in Thrace. Excavation resultsKrassimira Luka
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
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This presentation was provided by Rebecca Benner, Ph.D., of the American Society of Anesthesiologists, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
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1. Physics 121: Electricity &
Magnetism – Lecture 5
Electric Potential
Dale E. Gary
Wenda Cao
NJIT Physics Department
2. October 3, 2007
Work Done by a Constant Force
1. The right figure shows four situations in which a force is applied
to an object. In all four cases, the force has the same magnitude,
and the displacement of the object is to the right and of the
same magnitude. Rank the situations in order of the work done
by the force on the object, from most positive to most negative.
A. I, IV, III, II
B. II, I, IV, III
C. III, II, IV, I
D. I, IV, II, III
E. III, IV, I, II
F
I
F
II
F
III
F
IV
3. October 3, 2007
Work Done by a Constant Force
The work W done a system by
an agent exerting a constant
force on the system is the
product of the magnitude F of
the force, the magnitude Δr of
the displacement of the point
of application of the force, and
cosθ, where θ is the angle
between the force and
displacement vectors:
cos
r
F
r
F
W
F
II
F
III
r
F
I
r
F
IV
r
r
0
I
W
cos
r
F
WIV
r
F
WIII
r
F
WII
4. October 3, 2007
Potential Energy, Work and
Conservative Force
Start
Then
So
f
i
i
f
g
mgy
mgy
j
y
y
j
mg
r
F
W
]
ˆ
)
[(
ˆ
mgy
Ug
U
U
U
W f
i
g
g
i
f W
U
U
U
The work done by a conservative force
on a particle moving between any two
points is independent of the path
taken by the particle.
The work done by a conservative force
on a particle moving through any
closed path is zero.
yf
yi
r
g
m
5. October 3, 2007
The potential energy of the system
The work done by the electrostatic
force is path independent.
Work done by a electric force or “field”
Work done by an Applied force
Electric Potential Energy
Ui
Uf
W
U
U
U i
f
r
E
q
r
F
W
Ui
Uf
W
W
K
K
K app
i
f
W
Wapp
app
i
f W
U
U
U
6. October 3, 2007
2. In the right figure, we move the proton from point i to
point f in a uniform electric field directed as shown.
Which statement of the following is true?
A. Electric field does positive work on the proton; And
Electric potential energy of the proton increases.
B. Electric field does negative work on the proton; And
Electric potential energy of the proton decreases.
C. Our force does positive work on the proton; And
Electric potential energy of the proton increases.
D. Electric field does negative work on the proton; And
Electric potential energy of the proton decreases.
E. It changes in a way that cannot be determined.
Work: positive or negative?
E
i
f
7. October 3, 2007
The electric potential energy
Start
Then
So
The electric potential
Electric Potential
q
U
V
q
U
q
U
q
U
V
V
V i
f
i
f
s
d
F
dW
s
d
E
q
dW
0
s
d
E
q
W
f
i
0
f
i
i
f s
d
E
q
W
U
U
U
0
f
i
s
d
E
q
U
V
0
Potential difference depends only
on the source charge distribution
(Consider points i and f without
the presence of the test charge;
The difference in potential energy
exists only if a test charge is
moved between the points.
8. October 3, 2007
Just as with potential energy, only differences in electric potential are
meaningful.
Relative reference: choose arbitrary zero reference level for ΔU or ΔV.
Absolute reference: start with all charge infinitely far away and set Ui = 0,
then we have and at any point in an electric field,
where W is the work done by the electric field on a charged particle as that
particle moves in from infinity to point f.
SI Unit of electric potential: Volt (V)
1 volt = 1 joule per coulomb
1 J = 1 VC and 1 J = 1 N m
Electric field: 1 N/C = (1 N/C)(1 VC/J)(1 J/Nm) = 1 V/m
Electric energy: 1 eV = e(1 V)
= (1.60×10-19 C)(1 J/C) = 1.60×10-19 J
Electric Potential
W
U q
W
V /
9. October 3, 2007
uphill for
q
Electric field lines always point in the
direction of decreasing electric
potential.
A system consisting of a positive
charge and an electric field loses
electric potential energy when the
charge moves in the direction of the
field (downhill).
A system consisting of a negative
charge and an electric field gains
electric potential energy when the
charge moves in the direction of the
field (uphill).
Potential difference does not depend
on the path connecting them
Potential Difference
in a Uniform Electric Field
Ed
ds
E
V
V
V
f
i
i
f
f
i
f
i
f
i
i
f Eds
ds
E
s
d
E
V
V
V )
0
cos
(
f
c
f
c
f
c
i
f ds
E
ds
E
s
d
E
V
V 45
cos
)
45
cos
(
c
i
c
i
i
c ds
E
s
d
E
V
V 0
)
90
cos
(
Ed
q
V
q
U 0
0
Ed
d
E
V
V i
f
45
sin
45
cos
downhill for
+ q
10. October 3, 2007
Equipotential Surface
The name equipotential surface is given to any
surface consisting of a continuous distribution
of points having the same electric potential.
Equipotential surfaces are always perpendicular
to electric field lines.
No work is done by the electric field on a
charged particle while moving the particle along
an equipotential surface.
The equipotential surface is like the “height”
lines on a topographic map.
Following such a line means that you remain at
the same height, neither going up nor going
down—again, no work is done.
Analogy to Gravity
11. October 3, 2007
3. The right figure shows a family of equipotential surfaces
associated with the electric field due to some distribution of
charges. V1=100 V, V2=80 V, V3=60 V, V4=40 V. WI, WII, WIII
and WIV are the works done by the electric field on a charged
particle q as the particle moves from one end to the other. Which
statement of the following is not true?
A. WI = WII
B. WIII is not equal to zero
C. WII equals to zero
D. WIII = WIV
E. WIV is positive
Work: positive or negative?
12. October 3, 2007
Potential Due to a Point Charge
Start with (set Vf=0 at and Vi=V at R)
We have
Then
So
A positively charged particle produces a positive
electric potential.
A negatively charged particle produces a
negative electric potential
2
0
4
1
r
q
E
2
0
4
1
r
q
E
f
i R
f
i
i
f Edr
ds
E
s
d
E
V
V
V )
0
cos
(
r
q
r
V
0
4
1
)
(
R
q
r
q
dr
r
q
V
R
R
0
0
2
0 4
1
1
4
1
4
0
13. October 3, 2007
Potential due to
a group of point charges
Use superposition
For point charges
The sum is an algebraic sum, not a vector sum.
E may be zero where V does not equal to zero.
V may be zero where E does not equal to zero.
n
i
i
n
i
r
i
r
V
s
d
E
s
d
E
V
1
1
n
i i
i
n
i
i
r
q
V
V
1
0
1 4
1
q q
q -q
14. October 3, 2007
4. Which of the following figures have V=0 and
E=0 at red point?
Electric Field and Electric Potential
A
q -q
B
q q
q q
q q
C D
q
E
-q
q -q
-q q
15. October 3, 2007
Find an expression for dq:
dq = λdl for a line distribution
dq = σdA for a surface distribution
dq = ρdV for a volume distribution
Represent field contributions at P due to point
charges dq located in the distribution.
Integrate the contributions over the whole
distribution, varying the displacement as needed,
Potential due to a Continuous
Charge Distribution
r
dq
dV
0
4
1
r
dq
dV
V
0
4
1
16. October 3, 2007
A rod of length L located along the x axis has a uniform linear charge
density λ. Find the electric potential at a point P located on the y axis a
distance d from the origin.
Start with
then,
So
Example: Potential Due to
a Charged Rod
2
/
1
2
2
0
0 )
(
4
1
4
1
d
x
dx
r
dq
dV
dx
dq
d
d
L
L
d
x
x
d
x
dx
dV
V
L
L
ln
)
(
ln
4
)
(
ln
4
)
(
4
2
/
1
2
2
0
0
2
/
1
2
2
0
0
2
/
1
2
2
0
d
d
L
L
V
2
/
1
2
2
0
)
(
ln
4
17. October 3, 2007
According to Gauss’ law, the charge resides on the
conductor’s outer surface.
Furthermore, the electric field just outside the
conductor is perpendicular to the surface and field
inside is zero.
Since
Every point on the surface of a charged conductor
in equilibrium is at the same electric potential.
Furthermore, the electric potential is constant
everywhere inside the conductor and equal to its
value to its value at the surface.
Potential Due to
a Charged Isolated Conductor
0
B
A
A
B s
d
E
V
V
18. October 3, 2007
s
d
E
q
W
0
Suppose that a positive test charge q0 moves through a displacement ds
from on equipotential surface to the adjacent surface.
The work done by the electric field on the test charge is W = dU = -q0 dV.
The work done by the electric field may also be written as
Then, we have
So, the component of E in any direction is the negative
of the rate at which the electric potential changes with
distance in that direction.
If we know V(x, y, z),
Calculating the Field from the Potential
z
V
Ez
x
V
Ex
ds
E
q
dV
q )
(cos
0
0
ds
dV
E
cos
s
V
Es
y
V
Ey
19. October 3, 2007
Electric Potential Energy
of a System of Point Charges
Start with (set Ui=0 at and Uf=U at r)
We have
If the system consists of more than two charged
particles, calculate U for each pair of charges and
sum the terms algebraically.
r
q
V 1
0
4
1
r
q
q
V
q
U 2
1
0
2
4
1
)
(
4
1
23
3
2
13
3
1
12
2
1
0
23
13
12
r
q
q
r
q
q
r
q
q
U
U
U
U
W
Wapp
app
i
f W
U
U
U
W
U
U
U i
f
r
E
q
r
F
W
q1
q2
20. October 3, 2007
Summary
Electric Potential Energy: a point charge moves from i to
f in an electric field, the change in electric potential
energy is
Electric Potential Difference between two points i and f in
an electric field:
Equipotential surface: the points on it all have the same
electric potential. No work is done while moving charge
on it. The electric field is always directed perpendicularly
to corresponding equipotential surfaces.
Finding V from E:
Potential due to point charges:
Potential due to a collection of point charges:
Potential due to a continuous charge distribution:
Potential of a charged conductor is constant everywhere
inside the conductor and equal to its value to its value at
the surface.
Calculatiing E from V:
Electric potential energy of system of point charges:
W
U
U
U i
f
q
U
q
U
q
U
V
V
V i
f
i
f
r
q
r
V
0
4
1
)
(
n
i i
i
n
i
i
r
q
V
V
1
0
1 4
1
r
dq
dV
V
0
4
1
s
V
Es
z
V
Ez
x
V
Ex
y
V
Ey
r
q
q
V
q
U 2
1
0
2
4
1
f
i
s
d
E
q
U
V
0