Transcript Chapter 2 Motion Along a Straight Line Position, Displacement

FYI: School A must Topic
assume that
the force
"signal" travels infinitely fast,
6.2
Extended
to react to relative motion between the masses.
B – Electric field
FYI: School B assumes that the force "signal" is already in place in the
spacenormal
surrounding
the source
of the force.force,
Thus thetension
force signal
The
force,
the friction
anddoes
drag
NOTall
haveclassified
to keep traveling
the receiving
mass. occurring where
are
as to
contact
forces,
two
eachthat
other.
FYI: objects
Relativity contact
has determined
the absolute fastest ANY signal can
The
gravitational
electric force,
propogate
is c = 3.0108force,
m/s, the and
speedthe
of light.
however, do not need objects to be in contact (or even
close proximity). These two forces are sometimes
called action at a distance forces.
There are two schools of thought on action at a
distance.
School A: The masses know where each other are at
all times, and the force is instantaneously felt by
both masses at all times.
School B: The masses deform space itself, and the
force is simply a reaction to the local space,
rather than the distant mass.
Topic 6.2 Extended
B – Electric field
Thus School B is currently the "correct" view.
If,
for example, the gravitational forces were truly
"action at a distance," the following would occur:
SUN
c
c
The planet and the sun could not "communicate" quickly
enough to keep the planet in a stable orbit.
FYI: You have probably seen such a model at the museum. A coin is
Topicto be
6.2
Extended
allowed to roll, and it appears
in orbit.
B – isn't
Electric
field
FYI: Of course, if the slope
just right to match
the tangential speed,
the coin will spiral into the central maw.
Instead, look at the School B view of the space
surrounding the sun:
The planet "knows" which
way
the
the
the
to "roll" because of
local curvature of
space surrounding
sun.
Long distance
communication is not
needed.
FYI: The view of School B is
called the FIELD VIEW.
Topic 6.2 Extended
B – Electric field
Of course, if the mass isn't moving, it will roll
downhill if placed on the grid:
m0
m0
Depending on where we
place the "test" mass m0,
it will roll differently.
Question: Why is the arrow at the location of the first test mass smaller
than that at the second one?
Topic 6.2 Extended
B – Electric field
We can assign an arrow to each position surrounding
the sun, representing the direction the test mass
will go, and how big a force the test mass feels.
We represent fields with
vectors of scale length.
In the case of the
gravitational field, the
field vectors all point
toward the center:
Topic 6.2 Extended
B – Electric field
If we view our
gravitational field
arrows from above, we
get a picture that
looks like this:
What the field arrows tell
us is the magnitude and the
direction of the force on a
particle placed anywhere in
space:
The blue particle will
feel a "downward" force.
The red particle will feel
SUN
FYI: We don't even
have to draw the object
that is creating the field.
a "leftward" force whose
magnitude is LESS than that
of the blue particle.
6.2 SINKS.
Extended
FYI: Inward-pointing Topic
fields are called
Think of the field arrows
as water flowing into B
a hole.
– Electric field
FYI: Test charges are by convention POSITIVE. Therefore, field
Consider,
now, charge
a
vectors
For masses,
weshow the direction
around aall
charge
a POSITIVE
would
negative
charge:
have
is
an
attractive
want to go if placed in the field.
force.
SUN
-
All of the field
If we place a very small
arrows point inward.
POSITIVE test charge in
the vicinity of our
negative charge, it will
be attracted to the
center:
We can map out the
field vectors just as
we did for the sun.
Topic
6.2
Outward-pointing
fieldsan
areELECTRIC
calledExtended
SOURCES.
of the
FYI: We
call such a system
DIPOLE. Think
A dipole
hasfield
two
arrows(charges)
as water which
flowing
of
a fountain.
poles
in sign. field
Bareout
–opposite
Electric
Question:
T or F: Gravitational
fields are
sinks.
FYI:
The ELECTRIC
DIPOLE consists
ofalways
a source
and a sink.
We can place a negative
Question:isT or
F: Electric fields are always
sinks.
charge
positive.
charge
here.
Now suppose our
+
+
-
If we place a very small
The fields of the two
POSITIVE test charge in
the vicinity of our
positive charge, it will
be repelled from the
center:
We can map out the field
vectors just as we did
for the negative charge.
charges will interact:
Keep in mind that the
field lines show the
direction a POSITIVE
charge would like to
travel if placed in the
field.
A negative charge will do
the opposite:
Topic 6.2 Extended
B – Electric field
You may have noticed
that in the last field
diagram some of our
arrows were unbroken.
We can draw solid
field arrows as long as
we note that THE CLOSER
THE FIELD LINES ARE TO
ONE ANOTHER, THE
STRONGER THE FIELD.
+
-
FYI: There are some simple rules for drawing these solid "electric lines
of force."
Rule 1: The closer together the electric lines of force are, the stronger
the electric field.
strong
Rule 2: Electric lines of force originate on positive charges and end on
negative charges.
weak
Rule 3: The number of lines of force entering or leaving a charge is
proportional to the magnitude of that charge.
Topic
6.2 Extended
Question: Which charge
is the strongest
negative one? D
Question: Which charge
weakest positive
one?
E
B –is the
Electric
field
Question: Which charge is the strongest positive one?
A
Determine the sign and the magnitude of the
Question: by
Which
charge at
is the
weakest
negative
one? ofC force.
charges
looking
the
electric
lines
A
B
C
D
E
F
Topic 6.2 Extended
B – Electric field
So how do we define the magnitude of the electric
field vector E?
Here's how:
E =
F on q
q0
Electric field definition
o
where q0 is the positive test charge
Think of the electric field as the force per unit
charge.
To obtain a more useful form for E, consider the
force F between a test charge q0 and an arbitrary
kq0q
charge q:
F =
r2
kq
F on q = kq0q
E =
then
=
q0
q0r2
r2
so that
kq
Electric field in space
E =
r2
surrounding a point charge
o
Topic 6.2 Extended
B – Electric field
What is the magnitude of the electric field
strength two meters from a +100 C charge?
Use
kq
E =
r2
9109·10010-6
=
22
= 225000 n/C
What is the force acting on a +5 C charge placed
at this position?
From
E =
so that
F on q
q0
o
we see that
F = qE
= 510-6·225000
= 1.125 n
F = qE
Force on a
charge placed in
an electric field
Topic 6.2 Extended
B – Electric field
What is the electric field
at the chargeless corner of
the 2-meter by 2-meter
square?
+10
C
A
EB
EA
EC
C
C
B
Start by labeling the charges (organize your effort):
kq
kq
kq
|E
|
=
|EA| =
|E
|
=
C
B
r2
r2
r2
9109·1010-6
9109·1010-6
9109·1010-6
=
=
=
22
22
( 22+22 )2
= 22500 n/C
= 22500 n/C
= 11250 n/C
+10
C
-10
Now sketch in the field vectors:
Now sum up the field vectors:
E = EA + EB + EC
= 22500i + 11250 cos 45i + 11250 sin 45j - 22500j
= 30455i - 14545j (n/C)
Topic
6.2
Extended
FYI: The dipole electric
field drops
off by
1/x3 rather than inverse
square like a "monopole."
B – Electric field
What is the electric field along the bisector of a
distant dipole having a charge separation d?
A dipole is an equal positive and negative charge in
close proximity to one another:
+q
r
d


2
d
2
x
r
-q
kq
r2
Note that the horizontal components cancel, and the
vertical components add: |ETOTAL| = 2|E| sin .
Both field vectors have the same length:
But sin  = (d/2)/r = d/2r so that
|E| =
kqd
r3
But r = (d/2)2 + x2 . Since x >> d, r  x and we have
|ETOTAL| = 2|E| sin  =
EDIPOLE =
kqd
x3
Electric field far
from a dipole