Physics 2212
Quiz #1
Solutions
Fall 2009
²
0
Permittivity constant
m
p
Mass of a proton
μ
0
Permeability constant
m
e
Mass of an electron
e
Fundamental charge
c
Speed of light
K
Coulomb constant
g
Acceleration due to gravity
Unless otherwise directed, friction, drag, and gravity should be neglected, and all batteries and wires are ideal.
Any integrals in freeresponse problems must be evaluated.
I
. (16 points) The parallel plate capacitor (surface charge density
η
, side length
L
, distance
d
between the
plates; where
L
d
) shown below acts as a “velocity filter” for a beam of electrons that enters the capacitor
from the left centered between its plates, and moving initially straight to the right. That is, only electrons
entering with a certain speed
v
0
are able to leave the capacitor through a small hole in its lower plate at
distance
‘
from the left capacitor edge.
What is
v
0
? Express your answer in terms of parameters defined in the problem and physical or mathematical
constants.
.
.
.
.
.
.
.
.
.
.
.
.
There is no horizontal force on the electron, so its horizon
tal acceleration is zero. Because the electric field between
parallel plates with
L
d
is uniform, there is a constant
vertical force on the electron,
~
F
=
q
~
E
, so the vertical accel
eration is constant. This is essentially a projectile motion
problem. Choose a coordinate system, and then use con
stant acceleration kinematics in the horizontal and vertical
directions, linked by time.
Find the time for the electron to reach the hole from the horizontal (
x
) information:
x
=
x
0
+
v
0
x
(Δ
t
) +
1
2
a
x
(Δ
t
)
2
where
x
=
‘
,
x
0
= 0,
v
0
x
=
v
0
, and
a
x
= 0, so
‘
=
v
0
(Δ
t
)
⇒
Δ
t
=
‘
v
0
In the vertical (
y
) direction:
y
=
y
0
+
v
0
y
(Δ
t
) +
1
2
a
y
(Δ
t
)
2
where
y
=
d/
2,
y
0
= 0,
v
0
y
= 0, and (in terms of magnitudes)
a
y
=
F
y
/m
=
qE/m
=
eE/m
e
. Recall that
the electric field between two parallel plates is related to the area charge density on the plates,
E
=
η/²
0
.
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 Spring '09
 Kindermann
 Physics, Charge, Acceleration, Friction, Gravity, Mass, Light, Electric charge, charge density

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