Electric Forces and Electric Fields
Objective:
•Define and apply Coulomb’s Law to calculate
the electric force between charged particles.
•Plot electric field lines and calculate electric
fields for simple charge distributions.
Bellwork – please write the answer on your homework
1. A glass rod rubbed with silk acquires a charge of +8.0 x 10-10 C.
a) What is the charge on the silk and how many electrons
have been transferred to the silk?
b) How much mass has the glass rod lost?
2. Fiona is on her way home but must leave her new-found
love, Shrek, behind. As Fiona’s stallion takes off at 4 m/s,
Shrek tosses a bouquet of onion blossoms with a speed of 6
m/s. According to Fiona, how fast are the flowers when she
catches them?
3. In an attempt to separate the two, Fairy Godmother casts a
spell that speeds up the stallion to 70% the speed of light. It
takes 20 hours, according to Fiona’s watch (t0 ) to break the
spell. How long did it take according to Shrek’s clock?
Electric Charges Describe Forces
• The charge-force law gives the direction of the
force between charged particles
• Coulomb’s Law describes the magnitude of the
force between charged particles
Coulomb’s Law
• The magnitude of electrical force between
two point charges is directly proportional to
the product of the magnitude of the charges
themselves and inversely proportional to the
square of the distance between them.
• k is a constant whose experimental value was
determined by Coulomb to be
k=8.988x109 Nm2/C2 .
Sketching Free-Body Diagrams
Three point charges are placed along the x-axis. A +5 µC
charge is located at the origin, a +2 µC charge is located
30 cm to its right, and a -4 µC is located at 50 cm.
1. Calculate the magnitude and direction of the force
exerted on the +2 µc charge by the +5 µC charge.
2. Calculate the magnitude and direction of the force
exerted on the +2 µc charge by the -4 µC charge
3. What is the magnitude and direction of the net force
on the +2 µC charge?
Solutions
1. .
2. .
Solutions
3. Fe = 2.1 N to the right
This process of isolating each set of forces and then
adding together their results is called the
superposition principle
net F = 0.3 N + 1.8 N
net F = 2.1 N to the right
Examine the following diagram which shows four
charges that have been placed on the corners of a
square 50 cm on each edge. Determine the net
force on the 2 µC charge.
Problem-Solving Strategy
1. Sketch the free-body diagram to describe the
forces on the 2 μC charge
2. Calculate the magnitude and direction of F3,2
3. Calculate the magnitude and direction of F5,2
4. Calculate the magnitude and direction of F-4,2
5. Calculate the net force on the 2 µC charge in
both the x-direction and the y-direction
6. Calculate the final magnitude and direction of
the force on the 2 µC charge.
Free-Body Diagram
The magnitude and direction of F2,3
The magnitude and direction of F5,2
The magnitude and direction of F-4,2
Evaluate components of the net force
F
x
y
F5,2
0
0.36
F3,2
-0.216
0
F-4,2 0.144 cos 45º = 0.102 -0.144 sin 45º = -0.102
Fnet
-0.114 N
0.258 N
Calculate the final magnitude and direction of
the force on the 2 µC charge
Electric Fields
• An electric field is the region surrounding a
charged particle, Q, where another charged
particle with experience either a force of
attraction or repulsion
• The magnitude of the electric field strength, E, is
E= kQ/r2
• The SI Units are derived by:
(Nm2/C2)(C)(1/m2) = N/C
Rules for drawing electric field lines:
1. Closer lines mean a stronger field.
2. The field is tangent to the lines at every point.
3. Field lines start on positive charges and end
on negative charges.
4. The number of lines entering or leaving a
charge is proportional to the magnitude of the
charge.
5. Field lines never cross.
How many lines
would be drawn
around the
charge -1 ½ q?
Electric Field Lines for Configurations
of Two or More Charges
oppositely-charged particles
like-charged particles
Left is +, right is both are +
• Fields between oppositely charged particles are
attractive and are elliptical in shape; while fields
between similarly charged particles are repulsive and
hyperbolic in shape.
The Electric Field
• Charges create electric fields and these fields
exert electrical forces on other charges.
• The electric field direction is in the direction of
the force experienced by a positive test charge.
• The superposition principle: for a configuration
of charges, the total, or net, electric field at any
point is the vector sum of the electric fields due
to the individual charges.
Bellwork and Quiz Review
In a 4.00 g of helium, the nuclei are
separated from the electrons by a distance of
1 km. What is the magnitude of the electric
force between the protons and the
electrons?
Example: Electric Field in Two Dimensions Using
Vector Components and Superposition
Calculate the magnitude and direction of the
electric field at the origin due to these charges
Solution
• Use vector addition to add the electric field
vectors,
• Given:
q1 = -1.00 μC = -1.00 x 10-6 C
q2 = +2.00 μC = +2.00 x 10-6 C
q3 = -1.50 μC = -1.50 x 10-6 C
r1 = 3.50 m
r2 = 5.00 m
r3 = 4.00 m
E= kQ/r2
Electric Field Due to a Dipole
Electric Field Due to Parallel Plates: when two
parallel plates are connected across a battery, the
plates become charged and an electric field is
established between them.
• the direction of an electric field is defined as the
direction that a positive test charge would move.
• The electric field would point from the positive
plate to the negative plate.
• Since the field lines are parallel to each other, this
type of electric field is uniform
Warm-Up
1. In a certain organic molecule, the nuclei of two
carbon atoms are separated by a distance of 0.25
nm. What is the magnitude of the electric force
between them?
2. An elementary particle called a pion (π), has a
lifetime of 2.6 x 10-8 s (t0) when at rest. A) Will its
lifetime be longer or shorter as viewed from the
stationary frame of reference, if it is made to travel
at 80% the speed of light? B) What will its lifetime
be according to a stationary observer?
Learn more about pions and other fundamental
particles at http://particleadventure.org/
Conductors and Electric Fields
• The electric field is zero inside a charged
conductor
• Any excess charge on an isolated conductor
resides entirely on the surface of the conductor
• The electric field at the surface of a charged
conductor is perpendicular to the surface
• Electric charge tends to accumulate a sharp points,
or locations of highest curvature, on charged
conductors. As a result, the electric field is
greatest at such locations
Conductors carry charge
along the surface
Electric fields are strongest at locations along
the surface where the object is most curved
Place four evenly-spaced negative charges
along each line.
For each surface show the electric field lines
Diagram the electric field lines for the
following configuration of two objects.
Place arrows on your field lines.
Where would the field strength be equal? Sketch
a line of equipotential (like in the PHeT Sim)
• The field lines should be directed
from + to - or from the edge of
the slide to the - or from + to the
edge of the slide. Each field line
MUST have an arrowhead on it to
indicate such directions.
• At the surface of either object,
the field lines should be directed
perpendicular to the surface.
• There should be more lines at
the sharply curved and pointed
surfaces of the objects and less
lines at the flatter sections.
Gauss’s Law for Electric Fields
• The net number of electric field
lines passing through an imaginary
closed surface is proportional to
the amount of net charge enclosed
within that surface.
• The size and shape of the Gaussian
surface does not affect the total
number of field lines
• Gaussian Surfaces
(a) Surrounding a single positive
point charge,
(b) surrounding a single negative
point charge
Gaussian Surfaces, cont.
• Gaussian Surfaces
(c) surrounding a larger negative
point charge.
(d) Four different surfaces
surrounding various parts of an
electric dipole.
• The net charge within both
surfaces 3 and 4 is zero. Count
the positive and negative field
lines.
Conservation of Energy
• It would take work to move two like charges closer
together or to separate opposite charges
• How much work? Work = some force applied across
a given distance
• W = Fcosqd
• Energy is the ability to do work.
• W = DKE = KEfinal - KEinitial
Electric Potential
The Potential Energy (Work) to move charges
through an electrical field depends on:
1) Electric charge - a property of the object
experiencing the electrical field
2) Distance from source - the location within the
electric field
and
E V
d
Defining Charge
A piece of plastic has a net charge of + 2.00
nC. How many more protons than electrons
does this piece of plastic have? What mass
was lost by the plastic when it became
charged?
Electrical Forces: Applications of Coulomb’s Law
Two 1.2-gram balloons are suspended from light
strings attached to the ceiling at the same point.
The net charge on the balloons is -540 nC. The
balloons are distanced 68.2 cm apart when at
equilibrium. Determine the amount of tension on
the string.
Describing Electrical Fields
Several electric field line patterns are shown in
the diagrams below. Which of these patterns
are incorrect? Explain what is wrong with all
incorrect diagrams.
Electric Potential Difference
• Potential Difference: The work done to move a
positive test charge from one location to
another.
• SI Unit = volt, V
1Volt = 1Joule/1Coulomb
• Energy = ability to do work, so voltage is used
to describe the amount of electrical potential
energy PER test charge
Example Problem
An electron in Tammie’s TV is accelerated
toward the screen across a potential
difference of 22000 V. How much kinetic
energy does the electron lose when it strikes
the screen?
Example Problem
• Amir shuffles his feet across the living room
rug, building up a charge on his body. A spark
will jump when there is a potential difference
of 9000 V between the door and the palm of
Amir’s hand. This happens when his hand is
0.3cm from the door. At this point, what is the
electric field between Amir’s hand and the
door?
• HINT: E=V/d
Independent Practice
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p. 531 – 535; 28, 29, 40, 52,70, 77, 85
Finish “Electric Fields – Point Charges”
Review for Ch 15 Quiz Thursday
Set up your lab notebook to collect Egg Car Data
and update your journaling section. This is worth
20 points, so be thorough and include relevant
details in your observations and notes!
• Be ready for Egg Car Collisions Test Runs Friday!