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Assignment 07

# Assignment 07 - Class PEP112S2007 Assignment 7 Assignment...

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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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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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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: 3 1 none of the above: the cyberon will never reach the upper plate Because it has positive instead of negative charge, the cyberon will accelerate downward, toward the lower plate.
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