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Class PEP112S2007
Assignment 7
Assignment is due at 11:00pm on Tuesday, March 20, 2007
Credit for problems submitted late will decrease to 0% over the course of 10 hour(s) after the
deadline has passed.
The wrong answer penalty is 1% per part. Multiple choice questions are penalized as described in
the online help.
The unopened hint bonus is 1% per part.
You are allowed 10 attempts per answer.
The Fate of an Electron in a Uniform Electric Field
In this problem we will study the behavior of an electron in a uniform electric field. Consider a uniform
electric field
(magnitude
) as shown in the figure within a parallel plate capacitor in vacuum.
First, let us review the relationship between
an electric field and its associated electric
potential
. For now, ignore the electron
located between the plates.
Part A
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View Full Document Calculate the electric potential
inside the capacitor as a function of height
. Take the potential at
the bottom plate to be zero.
Hint A.1
Relationship of field and potential
Hint not displayed
Hint A.2
Limits of integration
Hint not displayed
Express
in terms of
and
.
ANSWER:
=
Now an electron of mass
and charge
(where
is a
positive
quantity) is placed within the electric
field (see the figure) at height
.
Part B
Calculate the electon's potential energy
, neglecting gravitational potential energy.
Hint B.1
Definition of electric potential energy
Hint not displayed
Express your answer in terms of
,
, and
.
ANSWER:
=
Part C
The electron, having been held at height
, is now released from rest. Calculate its speed
(i.e.,
)
when it reaches the top plate.
Part C.1
How to approach the problem
Part not displayed
Part C.2
Find the initial energy
Part not displayed
Part C.3
Find the final energy
Part not displayed
Express
in terms of
,
,
,
,
, and other given quantities and constants.
ANSWER:
=
Now we consider the effect of changing either the charge or the mass of the charged particle that is released
from rest at height
.
Part D
Imagine a particle that has three times the mass of the electron. All other quantities given above remain the
same. What is the ratio of the kinetic energy
that this heavy particle would have when it reaches
the upper plate to the kinetic energy
that the electron would have? That is, what is
?
Hint D.1
Energy conservation
Hint not displayed
ANSWER:
3
1
none of the above: the heavy particle will never reach the upper plate
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View Full Document Part E
Imagine a third particle, which we will call a cyberon. It has three times the mass of an electron (
). It
has a
positive
charge that is three times the magnitude (
) of the charge on an electron. What is the ratio
of the speed
that the cyberon would have when it reaches the upper plate after being released from rest
at position
to the speed
that the electron would have? That is, what is
?
ANSWER:
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This homework help was uploaded on 04/09/2008 for the course PEP 112 taught by Professor Whittaker during the Spring '07 term at Stevens.
 Spring '07
 Whittaker

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