Chapter 17:
Electric Forces
and Fields
Objectives
• Understand the basic properties of electric
charge.
• Differentiate between conductors and
insulators.
• Distinguish between charging by contact,
charging by induction, and charging by
polarization.
Electric Charge
•
•
•
•
•
protons have positive (+) charge
electrons have negative (–) charge
opposite charges attract; like charges repel
charge is always conserved (cannot be destroyed)
charge (q) is measured in coulombs (C)
Charles Augustin Coulomb
1736 - 1806
Electric Charge is Quantized
1909:
Robert Millikan
qE
+
mg
qE  mg Charge on drop
mg occurs in multiples
q
of 1.60 x 10-19 C
E
(±1e, ±2e, ±3e…).
Transfer of Electric Charge
• charges move freely through conductors
(typically metals)
• charges do not move freely in insulators
(most other solids)
Electric charge can be transferred 3 ways:
• contact
• induction
• polarization
Objectives
• Calculate electric force using Coulomb’s law.
• Compare electric force with gravitational
force.
Coulomb’s Law
m1  m2
FG  G 
r2
Law of Universal
Gravitation
q1  q 2
Fe  k 
r2
Coulomb’s Law
k = 8.99 x 109 Nm2/C2
Compare the gravitational and the
electric forces between the proton
and electron in a hydrogen atom.
Objectives
• Calculate electric field strength.
• Draw and interpret electric field lines.
• Identify the properties associated with a
conductor in electrostatic equilibrium.
Electric Fields
Field lines show direction and strength of force
(represented by the line density)
• gravitational field (g)
• electric field (E): (+) → (–)
Fg  m  g
g
Fg
m
Fe  q 0  E
Fe
E
q0
units are N/C
Electric Fields
The nucleus applies a force of 8.16 x 10-11N on the
electron in a hydrogen atom. What is the electric
field strength at the position of the electron?
Electric Field due to a Point Charge
q  q0
Fe  k  2
r
Fe
q  q0
E
 k 2
q0
r q0
q
E  k 2
r
(a) What is the E-field strength
at a distance of 0.45 m from a
8.2mC charge?
(b) What force would be felt
by a proton at this location?
(c) What is the initial
acceleration of the proton?
Conductors in
Electrostatic Equilibrium
electrostatic equilibrium: no
net motion of charge
(a) The total electric field
inside a conductor equals zero.
(b) Excess charge resides on the
surface.
(c) E-field lines extend
perpendicular to the surface.
(d) Charge accumulates at
points.
Chapter 18:
Electric Energy
and Capacitance
Electric Potential Energy (EPE)
ME  KE  PE grav  PEelastic  PEelectric
• uniform field only!
• displacement in direction of the field
PE grav  m  g  h
PE electric   q  E  d
g
E
EPE Problems
• What is the change in EPE if a proton is moved
2.5mm in the direction of a uniform 7.0 x1011 N/C
electric field?
• What is the change in EPE if an electron is moved in
the same direction?
EPE for a Pair of Charges
PE elec
PE elec
q1  q 2
 q  E  d  Fe  r  k 
r
2
r
q1  q 2
 k
r
• Two alpha particles (two helium nuclei, 2 p+ each)
have an EPE of 6.32 x10-19 J. What is the distance
between the two particles?
Potential Difference (Voltage)
PE grav  m  g  h
PE electric   q  E  d
PE grav
PE electric
 E  d
q
PE electric
" voltage" 
  E  d
q
V   E  d (uniform field only)
m
 gh
• voltage (V) is EPE per charge
• 1 volt = 1 J/C
• measured with a voltmeter
or multimeter
• voltage is like “electric pressure”
Voltage Problems
What voltage exists in a 3.5 x10-6 N/C electric
field between two points that are 0.25 m apart?
Capacitors
• Capacitors store EPE between
two closely-spaced conductors
that are separated by an
insulator.
• Capacitance is measured in
farads (F). 1 F = 1 C/V
Q
C
V
PE electric  21 Q  V
Chapter 19:
Electric Current and
Electric Power
Electric Current
Electric charges will flow between areas of different
electric potential (voltage)
• electric current (I): a flow of
electric charge
• 1 ampere (A) = 1 C/s
• measured with an ammeter
• although electrons typically flow, current is
defined as direction of positive flow (+ → –)
• drift speed of e– in Cu at 10 A is only 0.00025 m/s
• 0.005 A is painful and 0.070 A can kill you
Electric Resistance
• resistance (R): resistance
to electron flow
• measured in Ohms (Ω)
• V ↑, I ↑
• R ↑, I ↓
V
I
R
A 2400-Ω resistor is attached to a 12-V power
source. What is the current through the wire?
AC/DC
• alternating current: electric field
reverses periodically, current alternates
direction (60 hz in USA)
• direct current: field is constant,
current is constant
• batteries produce DC
• electric generators can make AC or DC
Electric Power and Energy
Consider the units
of voltage:
J
V
C
J  C V
J C V C

 V
s
s
s
W  A V
Pelec  I  V
E elec  I  V  t
Power Problems
If voltage = 120 V, what is the current through
a 1200-W hairdryer?
At $0.05 / kW·hr, how much does it cost to
operate a 240-W television for 24 hrs?