Exam 1 practice problems solutions

Exam 1 practice problems solutions - Exam #1 practice...

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Exam #1 practice problems solutions Physics 227 1. Have a look at the situation shown. A soda can is resting on a plastic stand. A piece of aluminum foil hangs vertically from a thread (an insulator) so it is touching the right side of the soda can. A glass sphere that has been rubbed with silk (so it becomes positive) is slowly moved closer to the left side of the can, eventually touching it briefly. It is then slowly moved away. a. Describe what, if anything, happens to the glass sphere, the soda can, and the aluminum foil throughout this entire situation. Give any explanation for what happens (or why nothing happens). b. Repeat part a., except with the soda can replaced with a plastic bottle. Since the soda can and aluminum foil are in contact they will behave like a single conducting object. When the sphere gets close to the soda can it draws electrons towards it, polarizing the can/foil. This results in an attractive force on the can/foil but will likely not overcome friction. Once the sphere touches the can it removes electrons from it. Now that the can/foil has a net positive charge, the can and foil will separate, repelling each other. This continues even after the sphere has been removed. If the can is replaced with a plastic bottle it will still polarize but even once it has become slightly positively charged (though only the left side of it) by the contact with the sphere the aluminum foil will remain neutral. Because of this the foil will remain in contact with the bottle at all times. 2. By accelerating electrons to extremely high speeds and firing them at nuclei we can probe the structure of the nucleus. By doing this particle physicists have determined that the radius of the proton is approximately 15 1.2 10 m . This is much smaller than the radius of an atom, which for hydrogen anyway, is approximately 11 5.3 10 m . Using this information, it’s possible to construct the following model of the hydrogen atom: The nucleus is a single proton which is going to be treated as a solid sphere of uniformly distributed positive charge with the radius stated above and total charge equal to the standard proton charge. The electron is not going to be treated as a particle. Instead it is going to be treated as an extended object, a thin spherical shell centered on the nucleus. It has the atomic radius stated above and total charge equal to the standard electron charge. a. What is the electric field outside of the atom as a function of distance ( r ) from the center of the nucleus. Explain your reasoning. Express your answer for all parts of this problem in terms of the charge on the proton ( e ), the radius of the nucleus ( 0 r ), and any other fundamental constants you need. b. What is the electric field between the nucleus and the electron shell as a function of distance ( r ) from the center of the nucleus. Explain your reasoning.
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Exam 1 practice problems solutions - Exam #1 practice...

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