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Electric Fields
Physics 12
Joke of
the day:
Clip of the day:
• More minute physics…maybe Ms R’s new
favorite thing on the internet!
• http://www.youtube.com/watch?v=3MqYE2Uu
N24&list=PLED25F943F8D6081C
Field Theory
• There are three common forces that act without
contact between objects:
▫ Gravitational
▫ Electrostatic
▫ Magnetic
• Since these forces do not require contact, field
theory is often used to describe the force that
results on an object within the field
Describing Fields
• Michael Faraday was credited as the first
person to first discover electrical fields.
• The fundamental concept is that a field is a
property of space.
• What is a field?
▫ An object influences the space around it by
creating an electric field, magnetic field, or a
gravitational field.
▫ A region around a charged particle or object
within which a force would be exerted on
other charged particles or objects.
An example you know:
• Recall force between two masses: F = m g
g is the gravitational field (9.81 m/s2)
Gravitational Field
• The strength of a gravitational
field can be determined using a
test mass
• Like with a test charge, the test
mass should be small
• In a manner similar to the
electric field, we divide out the
test mass
This is the gravitational
field intensity
Gmmt
Fg 
2
r
Fg Gmmt

2
mt
mt r
Fg
Gm
 2
mt
r

 Fg
g
mt
• An electric charge is surrounded by an electric
field just as a mass is surrounded by a
gravitational field.
Electric Field Mapping
• To map an electric field, a small test charge is
placed in the field and the magnitude and
direction of the force is recorded
• The test charge is then moved throughout the
electric field and a map of the field is created
• The force experienced by the test charge will be
the result of Coulomb’s Law
Test Charge
• The test charge that is used must be
small compared to the charge
creating the field
• If not, the test charge’s field will
change the field that is being
investigated
• The electric field should be the
same regardless of the test charge
used
• It is usually given the symbol q' (q
prime)
Electric Field Intensity
• is defined as the force per unit positive charge
that would be experienced by a "test charge", at
a given location in the field"
 Fonq'
E 
q'
Units = N
C
Test
charge
Note:
▫ The force is “felt” by the test
charge
▫ The electric field is from the
source charge
Electric field intensity or strength:
Direction of Electric Fields:
• The direction of the electric field produced by
the charge +Q is outward
• The direction of the electric field produced by
the charge -Q is inward
▫ Test charge is positive here!
Draw positive and negative sources
with a test charge that is negative:
Relationships between Force direction
and Electric Field direction:
• Positive test charge field's direction is in the
same direction as the force on the object.
• For a negative test charge, the force and the field
will have opposite directions.
Sample Problem 1:
•
A positive test charge, qt= 2.0 x 10-9, is placed in an electric
field and experiences a force of 4.0 x 10-9 N (west). What is the
electric field intensity at the location of the test charge?
Include a diagram.
• E=F
qt
= 4.0 x 10-9
2.0 x 10-9
= 2.0 N (west)
C
Try it :
• Page 646
▫ Questions 11-14
▫ Include a diagram for these questions
 Draw the source and test charges as well as indicate
the direction of the electric field and force with
arrow!
Drawing Electric Field Lines
Part 2
Electric Field Lines:
• A) The electric field lines from positive charge +q are
directed radially outward.
(B) The electric field lines are directed radially inward
toward negative point charge –q
Drawing electric field lines:
1. Electric field lines always extend from a
positively charged object to a negatively
charged object, from a positively charged
object to infinity, or from infinity to a
negatively charged object.
2. Electric field lines never cross each other.
3. Electric field lines are most dense around
objects with the greatest amount of charge.
4. At locations where electric field lines meet the
surface of an object, the lines are perpendicular
to the surface.
Field Intensity:
• The larger arrows represent stronger field strength.
• The distance from the particle follows the inverse
square law.
Field Lines – Two Opposing Charges
Field Lines – Two Positive Charges
Multiple Charges
• It is also possible to
consider what happens
with multiple charges:
Sample problem:
• What are the relative
magnitudes of the
charges in the diagram?
• What is the polarity of
each of the charges?
• Left =positive, right =
negative and left much
bigger charge then right
Review: Electric Field Intensity
• The electric field can be determined using the
force experienced by a particle and the charge
Source
on the particle
charge
 kq
E 
d
2
Practice Problems
• Page 655
▫ 20-26
Some practise multiple choice:
1. 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.
Answer: C, D and E
• In C, the lines are directed towards a positively
charged object.
• In D, the lines are not symmetrically positioned
despite the fact that the object is a symmetrical
sphere.
• In E, the lines are directed away from a negative
charge.
2. Ms R drew the following electric field lines for a
configuration of two charges. What did she do
wrong? Explain.
Answer:
• Electric field lines should never intersect each
other. Erin crossed his lines.
3. Consider the electric field lines shown in the diagram
below. From the diagram, it is apparent that object A
is ____ and object B is ____.
a.
b.
c.
d.
e.
+, +
–, +, -, +
insufficient info
Answer: D
• Electric field lines are directed towards object A
so object A must be negative. They are directed
away from object B so object B must be positive.
4. Use your understanding of electric field lines to
identify the charges on the objects in the
following configurations.
Answer:
• Objects A, C, F, G, H and I are positive.
• Objects B, D and E are negatively
charged.
• The principle is: electric field lines always
approach negatively charged objects and are
directed away from positively charged objects.
Applications of Electric Fields
Part 3
Sample Problem – Two Charges
• Two charges (A and B), -1.0μC and 2.0μC are
placed so the first(A) is at the origin and the
second is one meter to the right.
▫ Sketch the field lines and
▫ What is the electric field (magnitude and
direction) at the following locations
1.
2.
3.
4.
(0.5, 0)
(0.5, 1)
(0.25, 0.25)
(0.75, -0.25)
Practice Problem – Two Charges
• Two equal charges, 2.0μC are arranged so that
one (A) is at the origin and the other (B) is 0.5m
to the north. Sketch the field lines and then
determine the electric field (magnitude and
direction) at:
1.
2.
3.
4.
(1,0)
(15,15)
(0,-1)
(-1,-1)
Extra problem:
• A charge of 2.0mC is placed at the origin and a
charge of -5.0mC is placed at the point (3,0);
what electric field exists at:
▫ (1,0)
▫ (4,0)
▫ (-1,0)
• Where is the electric field equal to zero?