Field Theory Physics 12
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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 would look like.
Fields
There are three common forces that act without contact between objects:GravitationalElectrostaticMagnetic
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
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?
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
Multiple charges in a field
What would a field look like for one positively and one negatively charged particle?
Field Lines – Two Opposing Charges
How do I know the arrow points to the – not +?
Positively charged particles create outward arrows and vice versa
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 positive 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?
*** NOTES
More dense field lines means greater charge
Electric field lines never cross each other
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?
d
DAECB
Objects A, C, F, G, H and I are positive.
B < A C < D
G < E < FJ < H < I
Test Charge – Electric Field Intensity Formula
q is the charge of the sourceqt is the charge of the test
charge
Divide your electrostatic force formula by the test charge
E = Fe/qtThis is the electric field
intensity t
e
t
e
t
t
t
e
te
q
FE
r
kq
q
F
rq
kqq
q
Fr
kqqF
2
2
2
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.
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 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 646Questions 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)?
Comparing Forces
Gravitational Electrostatic Magnetic
Attractive Attractive or repulsive
Attractive or repulsive
Inverse square behaviour
Inverse square behaviour
Inverse square behaviour
Depends on mass
Depends on charge
Depends on pole strength
Comparing ForcesGravitational Electrostatic Magnetic
Weaker than other two
Lines go toward mass
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
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 massMagnetic 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
t
g
t
g
t
t
t
g
tg
m
Fg
r
Gm
m
F
rm
Gmm
m
Fr
GmmF
2
2
2
Practice Problems
Page 649Questions 15-18, 19*** (challenge – remember
centripetal acceleration!)
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