Phys 2180 Lecture (2)
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The Electric Field
Electric Field of a Continuous Charge Distribution
Electric Field Lines
Electric potential
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18.6 The Electric Field
As we know, a charge can experience an electrostatic force due to the presence of
other charges. This surrounding Force/Coulomb is known as the Electric Field
DEFINITION OF ELECRIC FIELD
The electric field that exists at a point is the electrostatic force experienced
by a small test charge placed at that point divided by the charge itself:

 F
E
qo
SI Units of Electric Field: newton per coulomb (N/C)
2
18.6 The Electric Field
Example 6 A Test Charge
The positive test charge has a magnitude of
3.0x10-8C and experiences a force of 6.0x10-8N.
(a) Find the electric field (force per coulomb) that
the test charge experiences.
(b) Predict the force that a charge of +12x10-8C
would experience if it replaced the test charge.
(a)
(b)
F 6.0 10 8 N

 2.0 N C
8
qo 3.0 10 C


F  2.0 N C 12.0 108 C  24 108 N
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18.6 The Electric Field
It is the surrounding charges that create the electric field at a given point.
The electrostatic force points in the direction of attraction
The electric field always points away from the positive charge and
towards the negative charge.
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18.6 The Electric Field
Example 7 An Electric Field Leads to a Force
The charges on the two metal spheres and the ebonite rod create an electric
field at the spot indicated. The field has a magnitude of 2.0 N/C. Determine
the force on the charges in (a) and (b)
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18.6 The Electric Field




(a)
F  qo E  2.0 N C 18.0 108 C  36 108 N
(b)
F  qo E  2.0 N C 24.0 108 C  48 108 N
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18.6 The Electric Field
Example 10 The Electric Field of a Point Charge
The isolated point charge of q=+15μC is
in a vacuum. The test charge is 0.20m
to the right and has a charge qo=+0.80μC.
Determine the electric field at point P.

 F
E
qo
F k
q1 q2
r2
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18.6 The Electric Field
F k
q qo
r2
8.99 10

9


N  m 2 C 2 15 10 6 C 0.80 10 6 C
0.20m 2

 2.7 N
F
2.7 N
6
E


3
.
4

10
NC
qo 0.80 10-6 C
q qo 1
F
E
k 2
qo
r
qo
The electric field does not depend on the test charge.
Point charge q:
Ek
q
r2
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7) Electric Field Lines (lines of force)
a) Direction of force on positive charge
radial for point charges
out for positive (begin)
in for negative (end)
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b) Number of lines proportional to charge
Q
2Q
c) Begin and end only on charges; never cross
E?
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d) Line density proportional to field
strength
Line density at radius r:
N
1

2  2
4r
r
Number of lines
area of sphere



Lines of force model <==> inverse-square law
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Electric Field Lines
Electric field lines always
begin on a positive charge
and end on a negative
charge and do not stop in
Mid-space.
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18.7 Electric Field Lines of two identical charges (dipoles)
The number of lines leaving a positive charge or entering a
negative charge is proportional to the magnitude of the charge.
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18.7 Electric Field Lines of two different charges
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Demonstration: Van de Graff generator
- purpose: to produce high field by concentrating charge -- used
to accelerate particles for physics experts
- principle: charge on conductors moves to the surface
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Electric Potential Energy is conservative
Gravitational force
Electrostatic force
Note: Electric energy is one type of energy.
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Reference Point of Electric Potential Energy
The reference point can be anywhere. For convenience,
we usually set charged particles to be infinitely
separated from one another to be zero potential energy
The potential energy U of the system at any point f is
where W∞ is the work done by the electric field on a charged
particle as that particle moves in from infinity to point f.
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Electric Potential
The electric potential difference V at a given
point is the electric potential energy U of a small
test charge q0 situated at that point divided by
the charge itself:
If we set
at infinity as our reference
potential energy,
SI Unit of Electric Potential: joule/coulomb=volt (V)
Note:
•Both the electric potential energy U and the electric
potential V are scalars.
•The electric potential energy U and the electric potential V
are not the same. The electric potential energy is associated
with a test charge, while electric potential is the property of
the electric field and does not depend on the test charge.
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The Electric Potential Difference
The electric potential difference between any two points i and f in
an electric field.
•
It is equal to the difference in potential energy per unit charge between the
two points.
• the negative work done by the electric field on a unite charge as that particle
moves in from point i to point f.
Note:
•Only the differences ΔV and ΔU are measurable in terms of the work W.
•The is ΔV property of the electric field and has nothing to do with a test charge
•The common name for electric potential difference is "voltage".
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Notes Continue
• Electric field always points from higher electric
potential to lower electric potential.
• A positive charge accelerates from a region of
higher electric potential energy (or higher
potential) toward a region of lower electric
potential energy (or lower potential).
• A negative charge accelerates from a region of
lower potential toward a region of higher
potential.
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24.3 Electric Potential:
The potential energy per unit charge at a point in an electric field is
called the electric potential V (or simply the potential) at that point.
This is a scalar quantity. Thus,
If we set Ui =0 at infinity as our reference potential energy, then the
electric potential V must also be zero there. Therefore, the electric
potential at any point in an electric field can be defined to be
Here W∞ is the work done by the electric field on a charged particle as
that particle moves in from infinity to point f.
The SI unit for potential is the joule per coulomb. This combination is
called the volt (abbreviated V).
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Problem
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Example 2 Work, Electric Potential Energy, and Electric
Potential
The work done by the electric force as the test charge (q0=+2.0×10–6 C)
moves from A to B is WAB=+5.0×10–5 J. (a) Find the difference, ΔU=UB–UA,
in the electric potential energies of the charge between these points. (b)
Determine the potential difference, ΔV=VB–VA, between the points.
W
V  VA  VB  
q
5  10 5 J

2  10 6
 25 V
U
 V  VA  VB 
q
 U  qV
 25V  (2  10 6 C )
 5  10 5 J
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Example 4 Electric Field and Electric Potential
Two identical point charges (+2.4×10–9 C) are fixed in place, separated by
0.50 m. Find the electric field and the electric potential at the midpoint
of the line between the charges qA and qB.
F
E
,
q
E  k
FAB   k
q A qB
r2
qA
r2
8.99  109 N  m 2 C 2 2.4  10 9 C

 345.22 N
2
0.50 / 2m 



V  VA  VB  Ed
0.5
2
 86.304 V
 345.22 
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Electric Potential
2.1 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:
Electric potential is defined as
potential energy per unit
charge:
Unit of electric potential: the volt (V).
1 V = 1 J/C.
2.1 Electrostatic Potential Energy
and Potential Difference
Electrical sources
such as batteries and
generators supply a
constant potential
difference. Here are
some typical potential
differences, both
natural and
manufactured:
2.2 Equipotential Surfaces
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.
2.2 Equipotential Surfaces
Example 23-10: Point
charge equipotential
surfaces.
For a single point charge
with Q = 4.0 × 10-9C,
sketch the equipotential
surfaces (or lines in a
plane containing the
charge) corresponding
to V1 = 10V, V2 = 20V,
and V3 = 30V.
2.2 Equipotential Surfaces
Equipotential surfaces are always
perpendicular to field lines; they are
always closed surfaces (unlike field lines,
which begin and end on charges).