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Essential University Physics
Richard Wolfson
20
Electric Charge, Force,
and Field
PowerPoint® Lecture prepared by Richard Wolfson
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-1
In Chapter 20 you learnt
• How matter and many of its
interactions are fundamentally
electrical
• About electric charge as a
fundamental property of
matter
• To describe the electric force
between charges
• The concept of electric field
• How to calculate the fields of
discrete and continuous charge
distributions
• How charges respond to electric
fields
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-2
Electric charge
• Electric charge is a fundamental property of matter.
• Many particles, including the electron and proton, carry electric
charge.
• Charge comes in two varieties, positive and negative.
• Most charged particles carry exactly one elementary charge, e,
either positive or negative.
• The proton carries exactly +e, the electron exactly –e.
• The quarks, which make up protons, neutrons, and other particles, carry
±1/3 e or ±2/3 e. But they’re never observed in isolation.
• The charge in a closed system is conserved, in that the
algebraic sum of charges remains unchanged.
• This is true even if new particles are created or destroyed.
• The SI unit of charge is the coulomb (C), equal to
approximately 6.25  1018 elementary charges.
• Thus e is approximately 1.6  10–19 C.
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-3
Coulomb’s law and the electric force
• Like charges repel, and opposite charges attract, with a
force that depends on
• The product of the two charges
• The inverse square of the distance between them
• Mathematically, the electric force is described by
Coulomb’s law:
kq1q2
F12  2 rˆ
r
Here F12 is the force q1 exerts
on q2 and rˆ is a unit vector
pointing from q1 toward q2 .
k is the Coulomb constant ,
9
2
2
approximately 9.0  10 N  m / C .
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-4
The superposition principle
• The electric force obeys the superposition principle.
• That means the force two charges exert on a third force is just
the vector sum of the forces from the two charges, each treated
without regard to the other charge.
• The superposition principle makes it mathematically
straightforward to calculate the electric forces exerted by
distributions of electric charge.
• The net electric force is the sum of the individual forces.
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-5
Clicker question
•
A charge q1 is located at x 1 m , y0. What should you use
for the unit vector r in Coulomb’s law if you are calculating
the force that q1 exerts on charge q2 located at the point x  0,
y 1 m?
A.

2ˆ
2 ˆ
i
j
2
2
2ˆ
2 ˆ
i+
j
2
2
B.
C.

2ˆ
2 ˆ
i
j
2
2
D.

2ˆ
2 ˆ
i+
j
2
2
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-6
Clicker question
•
A charge q1 is located at x 1 m , y0. What should you use
for the unit vector r in Coulomb’s law if you are calculating
the force that q1 exerts on charge q2 located at the point x  0,
y 1 m?
A.

2ˆ
2 ˆ
i
j
2
2
2ˆ
2 ˆ
i+
j
2
2
B.
C.

2ˆ
2 ˆ
i
j
2
2
D.

2ˆ
2 ˆ
i+
j
2
2
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-7
The electric field
• The electric field at a point in space is the force per unit
charge that a charge q placed at that point would
experience:
F
E
q
• The force on a charge
q in an electric field E
is F  qE.
• The electric field is
analogous to the
gravitational field,
which gives the force
per unit mass.
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-8
Fields of point charges and charge
distributions
• The field of a point charge
is radial, outward for a
positive charge and inward
for a negative charge.
Epoint charge
• The superposition
principle shows that the
field due to a charge
distribution is the vector
sum of the fields of the
individual charges.
kq
 2 rˆ
r
E   Ei  
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
kqi
rˆ
2 i
ri
Slide 20-9
The dipole: an important charge distribution
• An electric dipole consists of two point charges of equal
magnitude but opposite signs, held a short distance apart.
• The dipole is electrically
neutral, but the separation of
its charges results in an
electric field.
• Many charge distributions,
especially molecules, behave
like electric dipoles.
• The product of the charge and
separation is the dipole
moment: p = qd.
• Far from the dipole, its
electric field falls off as the
inverse cube of the distance.
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-10
Continuous charge distributions
• Charge ultimately resides on individual particles, but it’s
often convenient to consider it distributed continuously
on a line, over an area, or throughout space.
• The electric field of a charge distribution follows by
summing—that is, integrating—the fields of individual charge
elements dq, each treated as a point charge:
k dq
  dE   2 rˆ
r
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-11
Clicker question
•
Far from a dipole, you measure an electric field strength
of 800 N/C. If you double your distance from the
dipole, what will the electric field strength be at your
new location?
A. 400 N/C
B. 200 N/C
C. 100 N/C
D. 50 N/C
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-12
Clicker question
•
Far from a dipole, you measure an electric field strength
of 800 N/C. If you double your distance from the
dipole, what will the electric field strength be at your
new location?
A. 400 N/C
B. 200 N/C
C. 100 N/C
D. 50 N/C
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-13
Two examples
• The electric field on the axis of a charged ring:
Eon axis 
x
kQx
2
a

2 32
iˆ
• The electric field of an infinite line of charge:
• The line carries charge density  C/m:
2k 
E
y
direction radially outward
for + charge;
inward for – charge
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-14
Matter in electric fields
• For a point charge q in an electric field E , Newton’s law
and the electric force combine to give acceleration:
q
a E
m
• A dipole in an electric
field experiences a torque
that tends to align the
dipole moment with the
field:   p  E.
• If the field is not uniform,
the dipole also experiences
a net force.
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-15
Clicker question
•
A proton, an electron, a carbon-13 nucleus (6 protons, 7
neutrons), and a helium-4 nucleus (2 protons, 2 neutrons)
all find themselves in a uniform electric field. Which of
these particles exhibits the second-highest acceleration?
Assume that the mass of a proton equals the mass of a
neutron.
A. The proton
B. The carbon-13 nucleus
C. The electron
D. The helium-4 nucleus
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-16
Clicker question
•
A proton, an electron, a carbon-13 nucleus, and a
helium-4 nucleus all find themselves in a uniform
electric field. Which of these particles exhibits the
second-highest acceleration? Assume that the mass of a
proton equals the mass of a neutron.
A. The proton
B. The carbon-13 nucleus
C. The electron
D. The helium-4 nucleus
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-17
Conductors, insulators, and dielectrics
• Materials in which charge is free to move are conductors.
• Materials in which charge isn’t free to move are
insulators.
• Insulators generally contain molecular dipoles, which
experience torques and forces in electric fields.
• Such materials are called dielectrics.
• Even if molecules aren’t
intrinsically dipoles, they
acquire induced dipole
moments as a result of electric
forces stretching the molecule.
• Alignment of molecular
dipoles reduces an externally
applied field.
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-18
Summary
• Electric charge is a fundamental property of matter.
• Charge comes in two varieties, positive and negative.
• Charge is conserved.
kq q
• The force between two charges is given by Coulomb’s law: F12  12 2 rˆ.
r
• The electric force obeys the superposition principle, meaning the
forces due to individual charges sum vectorially.
• The electric field describes the force per unit charge at a given
point: E  F q .
kq
E
rˆ.
• The field of a dipole follows from Coulomb’s law:
r
• The fields of discrete charge distributions are calculated by summation.
• The fields of continuous charge distributions are calculated by integration.
2
• A point charge experiences a force F  qE in an electric field.
• A dipole experiences a torque in an electric field, and a force if the
field is not uniform.
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-19
Read Problem-Solving Strategy for using Coulomb’s Law on p 330
Interpret: identify the source charge
Develop:
draw coordinates and position of charges
determine unit vectors (are any along the axes?)
Evaluate: using Coulomb’s law remembering force is a vector
Assess:
is the force in the direction you expect for the sign of
the charges?
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-20
Problem 44
In the figure take q1 = 25 μC and q2 = 20 μC. If the
force on q1 points in the −x direction,
(a) what is q3 and
(b) what is the magnitude of the force on q1?
Copyright © 2007 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Slide 20-21