Transcript Slide 1

Electrostatic Force Field
“If there is onethey have to come (or go)!”
Pre-presentation Self Assessment Activity
Your comfort level with your
responses to the following two
question assessment tool should
indicate if the presentation that
follows will increase you
knowledge base on the topic
outlined by the questions in this
tool.
“If there is one- they have to come (or go)!”
Pre-presentation Self Assessment Activity
Problem #1:
Using the reference graphic shown below, develop a model that will
predict the coordinate position when the electron is exiting the
electrostatic field.
(Assume that the electron’s horizontal velocity has a constant value while
the electron is in the electrostatic field. Also assume that “d” is the
distance between the two charged plates.)
+z
ux
0
Va
e-
y
L
x
Vb
-z
+
the horizontal length of
the electrostatic field.
“If there is one- they have to come (or go)!”
Pre-presentation Self Assessment Activity
Problem #2:
Using your answer from review problem #1, develop the
model equation that will predict the electric field needed to
have the electron collide with the upper charged plate just as
the electron is leaving the electric field.
+z
ux
0
Va
e-
y
L
x
Vb
-z
+
the horizontal length of
the electrostatic field.
Electric force field
and
the resultant motion
“If there is one- electrons have to come (or go)!”
When a force exists where it exists is called
a force field
For engineers and technicians it is usually
very convenient to describe the force field
instead of the force.
“If there is one- they have to come (or go)!”
Electric Field between two charged Plates
Magnitude of Electric
field strength
Electric field
strength vector
[
E= [
-1
E= (4peo) (q1)
V
R
2
1,2
d
] Newton/Coulomb
] Volts/meters
By historic definition, voltage change occurs because
positive charge moves from higher energy environment to
lower energy environment.
z
(
)=
V = Vb - Va
where
Vb
dv
is the sum of all of the infinitesimal
voltage changes as the positive test
charge moves from Va to Vb.
Va
+
-
felectric
felectric
f dl
x
y
dv
] (q)
= - [dv/dl] (q)
=
=
-[
E
- [dv] (q)
As the charge moves an infinitesimal
distance in the electrostatic field the
voltage value changes an infinitesimal
amount.
dv =
-(
1
q
) f dl
dv =
-(
f
)
q
q= edv =
( E ) dl
dl
“If there is one- they have to come (or go)!”
Electron in an Electrostatic Field
Change in velocity
Change in
time
if an electron is accelerating then its
velocity is changing all the time.
du = a dt
x
x
electron accelerates
along the “x” direction
toward positive plate
Newton’s model as developed for distance traveled
by an object with mass in a uniform gravitational
force field. (same or opposite direction as field
lines)
x=
z
E
Vb
2
2
a x t + u0 t + x 0
This acceleration term is for
the acceleration of gravity
Va
e-
Distance traveled model for electron moving in the
x direction in a uniform electrostatic force field.
+
-
1
x=
1
2
2
a x t + u0 t + x 0
x
y
This acceleration term is for the
acceleration of the electron in
the electrostatic field.
“If there is one- they have to come (or go)!”
Electron in Electrostatic Field
Newton discovered that in a gravitational
field the force (the objects weight) was
proportional to the objects mass.
force
m
Gravitational force = a x m
electron accelerates
along the “x” direction
toward positive plate
mass of the
object
This acceleration term is constant
as long as the gravitational field
strength is constant.
z
Since both gravitational and electrostatic forces follow an inverse square distance relationship, by
analogy:
E
Vb
Electrostatic force = ax me
Va
e-
+
-
This acceleration term is
constant as long as the
electrostatic field
strength is constant.
Electrostatic force = E q
E q = ax m e
x
ax =
charge to mass ratio
y
mass of the
electron
q
m
( )E
“If there is one- they have to come (or go)!”
Electron in Electrostatic Field
Electrostatic force = ax me
mass of the
electron
This acceleration term is
constant as long as the
electrostatic field
strength is constant.
electron accelerates
along the “x” direction
toward positive plate
electron velocity in the
x direction of the
electric field.
z
E
Vb
x =
+
-
(
q
E t +u
m
0
)
current position of electron in
“x” direction when the electron
started at negative plate.
Va
e-
ux =
t2
[(
t1
q
E t +u
m
0
)
] dt
(When t = 0)
1
x
1
x =
2
y
(
2
q
E t + u t 0+x 0
m
)
“If there is one- they have to come (or go)!”
Electron in Electrostatic Field
Typical situation:
An electron in a vacuum environment
has a constant velocity, ux , in the x
direction and is about to enter an
electrostatic field as shown below.
+z
ux
0
Va
e-
+
y
x
Vb
-z
What is the predicted path of the
electron as it travels through the
electric field if the horizontal
velocity, ux, remains constant?
“If there is one- they have to come (or go)!”
In this situation, the electron will be
directed up (in the +Z direction) as it
moves through the electric field in the
X direction.
Electron in Electrostatic Field
Typical situation:
An electron in a vacuum environment
has a constant velocity, ux , in the x
direction and is about to enter an
electrostatic field as shown below.
+z
ux
0
Va
e-
+
e-
Electron distance traveled in the Z
direction as a function of the time
the electron is in the electric field.
z =
1
2
(
2
q
E t + u t 0+z
m
)
0
y
x
Vb
-z
What is the exact path the electron
will travel as it goes through the
electric field?
From the co-ordinate system
for this situation: z = 0
0
1
z =
2
(
2
q
E t + u t0
m
)
Note:
Setting zo = 0 allows the model to
follow the position of the electron as it
enters half way between the top and
the bottom charged plates.
“If there is one- they have to come (or go)!”
In this case, while the electron is in
the electric field it will move in the
up (+z) while it moves to the right.
Electron in Electrostatic Field
Typical situation:
An electron in a vacuum environment
has a constant velocity, ux , in the x
direction and is about to enter an
electrostatic field as shown below.
+z
ux
0
Va
e-
A) Model for upward motion.
1
+z
z =
=
2
(
2
q
E t + u t0
m
)
B) Model for motion to the right.
+
ux = a constant value = u0
y
x
Vb
-z
What is the exact path the electron
will travel as it goes through the
electric field?
x =
t2
t1
(u0) dt
Electron distance traveled
in the “x” direction.
x = u0 t
When t1 =0
“If there is one- they have to come (or go)!”
In this case, while the electron is in
the electric field it will move in the
up (+z) while it moves to the right.
Electron in Electrostatic Field
Typical situation:
An electron in a vacuum environment
has a constant velocity, ux , in the x
direction and is about to enter an
electrostatic field as shown below.
0
Travel upward.
1
+z
z =
=
2
+z
ux
C) Model for combined motion.
Va
e-
+
(
2
q
E t + u t0
m
)
Travel to the right.
y
x
Vb
-z
What is the exact path the electron
will travel as it goes through the
electric field?
x = u0 t
or t =
x
u0
Actual (x,z) position of electron as
a function of time
z - (t)= 1
e
2
(
q
E
m
When t0 = 0
x 2
) ( u0)
“If there is one- they have to come (or go)!”
Electron in Electrostatic Field
z - (t)= 1
e
2
q
E
m
(
ux
0
(remember that for constant speed
in the x direction,
x = u0? t )
time “x” position
+z
Va
t in
sec
+
y
e-
x = u0 t
“z” position
2
z(x)= [ q E ]x
2mu0
2
x
Vb
-z
1
2
)( )
Typical situation:
An electron in a vacuum environment
has a constant velocity, ux , in the x
direction and is about to enter an
electrostatic field as shown below.
x
u0
2
3
Time (seconds)
4
t0 =0 x 0= u 0 t 0 =0 z(x)= K( u x )= 0
0 0
2
t1 =1 x1 = u 0 (1)
2
z(x)=K(u 0 1) =1 u 0 K
t2 =2 x2 = u 0 (2)
2
z(x)=K(u 0 2) =4 u 0 K
t3 =3 x3 = u 0 (3)
2
z(x)=K(u 0 3) =9 u 0 K
2
2
Note:
K=
(
qE
2 mu
0
)
“If there is one- they have to come (or go)!”
Electron in Electrostatic Field
(
z - (t)= 1
e
2
q
E
m
x
u0
)( )
Typical situation:
(remember that for constant speed
in the x direction,
x = u0? t )
+z
2
Ku 0
0
2
Va
t in
sec
+
y
e-
x
u0
Vb
-z
1
2
3
Time (seconds)
4
x
u0
z(x)
2
Ku 0
0
1
2
3
4
5
6
0
1
2
3
4
5
6
0
1
4
9
16
25
36
t
t
t
2
qE
2 mu
0
)
Note:
K=
(
“If there is one- they have to come (or go)!”
Electron in Electrostatic Field
(
z - (t)= 1
e
2
q
E
m
x
u0
2
)( )
Typical situation:
The data indicates a parabolic path
t in
sec
+z
2
Ku 0
0
Va
+
y
e-
x
u0
Vb
-z
1
2
x
u0
Time (seconds)
4
2
Ku 0
0
1
2
3
4
5
6
0
1
2
3
4
5
6
0
1
4
9
16
25
36
t
t
t
2
qE
2 mu
0
)
Note:
3
z(x)
K=
(
“If there is one- they have to come (or go)!”
Electron in Electrostatic Field
Note:
Vd
E=(
d
)
Vd = Vb - V a
The data indicates a parabolic path
d is the distance between
the two charged plates.
+z
2
Ku 0
Va
+
e-
y
x
u0
0
Vb
-z
1
2
3
Time (seconds)
4
t in
sec
x
u0
z(x)
2
Ku 0
0
1
2
3
4
5
6
0
1
2
3
4
5
6
0
1
4
9
16
25
36
t
t
t
2
2
1
q
1
V
d
z(x)= ( )(
x)
)
(
)(
)
(
m
u0
2
d
“If there is one- they have to come (or go)!”
Pre-presentation Self Assessment Activity
Problem #1:
Using the reference graphic shown below, develop a model that will
predict the coordinate position when the electron is exiting the
electrostatic field. Assume that the electron’s horizontal velocity has a
constant value while the electron is in the electrostatic field. Also assume
that “d” is the distance between the two charged plates.
+z
ux
0
Va
e-
y
+
L
x
Vb
-z
Write your answer down before you
proceed.
the horizontal length of
the electrostatic field.
“If there is one- they have to come (or go)!”
Post-Presentation Self Assessment Activity
Problem #1:
Using the reference graphic shown below, develop a model that will
predict the coordinate position when the electron is exiting the
electrostatic field. Assume that the electron’s horizontal velocity has a
constant value while the electron is in the electrostatic field. Also assume
that “d” is the distance between the two charged plates.
+z
ux
0
Va
e-
y
(
+
)
( Vdd)
x
1
u0
2
( )(L)
L
Vb
-z
1
q
z(x)= ( )
m
2
the horizontal length of
the electrostatic field.
“If there is one- they have to come (or go)!”
Post-Presentation Self Assessment Activity
Problem #2:
Using your answer from review problem #1, develop the model equation
that will predict the electric field needed to have the electron collide with
the upper charged plate just as the electron is leaving the electric field.
+z
ux
0
Va
e-
y
+
)(
Vd
q
m) d
( )
2
1
( u )(L)
0
L
x
Vb
-z
z(x)= (
1
2
the horizontal length of
the electrostatic field.
“If there is one- they have to come (or go)!”
Post-Presentation Self Assessment Activity
Problem #2:
Using your answer from review problem #1, develop the model equation
that will predict the electric field needed to have the electron collide with
the upper charged plate just as the electron is leaving the electric field.
+z
ux
0
Va
e-
y
z(x)= (
+
1
2
)(
Vd
q
m) d
( )
2
1
( u )(L)
0
L
x
Vb
-z
Write your answer down before you
proceed.
the horizontal length of
the electrostatic field.
“If there is one- they have to come (or go)!”
Post-Presentation Self Assessment Activity
Problem #2:
Using your answer from review problem #1, develop the model equation
that will predict the electric field needed to have the electron collide with
the upper charged plate just as the electron is leaving the electric field.
+z
ux
0
Va
e-
y
z(x)= (
+
1
2
)(
Vd
q
m) d
( )
2
1
( u )(L)
0
L
x
the horizontal length of
the electrostatic field.
Vb
2
1
q
1
-z
= z(x) ( )(
L)
(
)
)
(
)
(
m
u0
2
Since the distance “d” between the d
Vd
plates is fixed the only variable
available is the electric field strength.
[
-1
]
“If there is one- they have to come (or go)!”
Post-Presentation Self Assessment Activity
Problem #2:
Using your answer from review problem #1, develop the model equation
that will predict the electric field needed to have the electron collide with
the upper charged plate just as the electron is leaving the electric field.
+z
ux
0
Va
e-
+
y
L
d
x
Note:
The charge, “q”, on a
-19
Coulomb
single electron =1.6 x10
The mass, “m”, of a
-31
kg
single electron =9.1 x10
d
=
2
Vd
( )=
d
[
9.1 d u0
2
1.6 L
-1
]
the horizontal length of
the electrostatic field.
Vb
-z
2
1
q
1
( 2 )( m )( u )(L)
0
( ) ( )[
Vd
] x 10
-12
“If there is one- they have to come (or go)!”
End of Presentation
Things to really remember:
1) The definition of E including its units.
2) The name for E.
3) The direction of E.
4) The charge (in Coulomb) on a single electron.
5) The unit of force in an electrostatic field.
Run this presentation over (and over) until
you at least remember these 5 things.
End of Presentation