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Field Theory
Physics 12
Field Theory
When forces exist without contact, it can
be useful to use field theory to describe
the force experienced by a particle at any
point in space.
We have previously considered
gravitational fields and seen that
gravitational fields are the result of mass
creating the field and the distance an
object is placed from the mass.
Draw a diagram of what you think a
gravitational field on Earth would look like.
Use rays to show direction.
Fields
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 (ie, not touching).
How do we know what a field looks like
then???
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 is a positive charge (and small – so
as not to affect the overall charge too much).
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.
Imagine a positively charged particle…
Electric Field Mapping
If a positive charge was put in this field, it
would repel (outward arrows).
As you get farther from
the charged particle, the
repulsion gets less and
less.
The arrows represent the
FORCE.
What would a negatively charged
particle’s field look like?
*** NOTES
More dense field lines means greater
charge
Electric field lines never cross each other
Multiple charges in a field
 What would a field look like for one positively and one
negatively charged particle?
Field Lines – Two Opposing Charges
What do you think…
Will happen when two positive charges of
equal strength are put together? What will
the field look like?
Field Lines – Two Positive Charges
What do you think…
Will happen when two negative charges
are put together? What will the field look
like?
Problem
 What are the relative
magnitudes of the
charges in the
diagram?
 What is the polarity of
each of the charges?
The left one is larger strength as there are more lines
from it. It is a positive charge as the arrows go away
from it. The right charge is weaker and negative.
Multiple Charges
 It is also possible to
consider what
happens with multiple
charges:
Check Your Understanding
1.Several electric field line patterns are
shown in the diagrams below. Which of
these patterns are incorrect? Why?
C, D, E
Check Your Understanding
2. What is wrong with this diagram?
Field lines are
crossed
d
DAECB
5. Use your understanding of electric field lines to
identify the charges on the objects in the following
configurations.
Objects A, C,
F, G, H and I
are positive.
6. Observe the electric field lines below for various configurations.
Rank the objects according to which has the greatest magnitude of
electric charge, beginning with the smallest charge.
B<A
C<D
G<E<F
J<H<I
Test Charge – Electric Field Intensity
Formula
kqqt
 q is the charge of the source
Fe  2
 qt is the charge of the test
r
charge
Fe kqqt

2
qt qt r
 Divide your electrostatic
force formula by the test
charge
 E = Fe/qt
 This is the electric field
intensity
Fe kq
 2
qt r

 Fe
E
qt
Where …
E = electric field intensity (N/C)
FQ = Fe = electric force (N)
qt = Electric charge (C) of test charge
Field Intensity at a Point
Example 1: A positive charge of
3.2 x 10-5 C experiences a force of 4.8N
right when placed in an electric field. Find
the magnitude and direction of the field, at
that location.
Draw a picture of what this might look like.
Hint… there are 2 answers 
Example 2
A positive test charge, qt = + 2.0 x 10-9 C,
is placed in an electric field and
experiences a force of F = 4.0 x 10-9 N
[W].
A) What is the electric field intensity
(magnitude) at the location of the test
charge?
B) Predict the force that would be
experienced by a charge of +9.0 x 10-6 C if
it replaced the test charge.
Answer
Practice Problems
Page 646
Questions 12-14
So what do you think would happen…
If we wanted a diagram of Earth and Moon
(gravitational charge instead of
electrostatic)?
What do you think…
A field would look like
around a “regular” magnet
(one North and one South
pole)? Consider North as
positive.
Comparing Forces
Gravitational
Electrostatic
Magnetic
Attractive
Attractive or
repulsive
Inverse square
behaviour
Depends on
charge
Attractive or
repulsive
Inverse square
behaviour
Depends on
pole strength
Inverse square
behaviour
Depends on
mass
Comparing Forces
Gravitational
Electrostatic
Magnetic
lines run out of a
positive charge
and into a
negative charge
lines are actually
closed loops
running out of a
north pole and
into a south pole
(if a dipole
magnet)
- North is like + if
monopole ***
Weaker than
other two
Lines go toward
mass
Field Lines Summary
 Graphical representation of the field
surrounding a point charge/mass or series of
charges/poles
 Electric fields: lines run out of a positive charge
and into a negative charge
 Gravitational fields: lines all go toward a mass
 Magnetic field lines: lines are actually closed
loops running out of a north pole and into a
south pole
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 will divide
out the test mass
Gmmt
Fg 
2
r
Fg Gmmt

mt r 2
mt
Fg
Gm
 2
r
mt

 Fg
g
mt
Practice Problems
Page 649
Questions 15-17