SEWANEE PHYS 104 - Matter & Interactions 2d Edition

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Matter & Interactions 2d EditionTest Question ArchivePreliminary versionCh 15November 28, 2007Caveat utilitor : RAW FILES, NOT EDITEDThese files are preliminary: the problems for this chapter have not been edited or proofread. Use at yourown risk.You may encounter issues such as• Missing diagram files• LATEXerrors• Textbook problems included• Problems assigned to the wrong chapter• Equation sheet missing or not appropriate for this chapter1015-002A very thin glass rod 4 meters long is rubbed all over with a silk cloth. It gains a uniformly distributedcharge +1.3x10−6C. Two small spherical rubber balloons of radius 1.2 cm are rubbed all over with wool.They each gain a uniformly distributed charge of -2x10−8C. The balloons are near the midpoint of theglass rod, with their centers 3 cm from the rod. The balloons are 2 cm apart (4.4 cm between centers).(a) Find the magnitude of the electric field at the location marked by the x, 0.6 cm to the right of thecenter of the left balloon. Also calculate the angle the electric field makes with the horizontal. Show allyour work, including showing vectors. State any approximations you are making.(b) A hydrogen atom is placed at that location (marked by the x). Draw a diagram showing the effect onthe hydrogen atom while it is at that location. The polarizability of atomic hydrogen has been measuredto be 7.4x10−41m3(Nm2/C2)−1. What is the distance between the center of the proton and the center ofthe electron cloud?2015-003A plastic ballpoint pen of length 14 cm is rubbed all over withwool and acquires a charge of -3x10−8coulombs, distributedmore or less evenly over the surface of the pen. A solid alu-minum ball suspended from an insulated string is touched to aVan de Graaff generator and acquires a charge of -2x10−9C.The charged ball is brought near the pen, as shown in the dia-gram. (The ball is held in place by the insulating string, whichis not shown in the diagram). The center of the ball is 3 cmfrom the pen.(a) On the diagram at right, clearly show the distribution ofcharge in and/or on the aluminum ball.(b) On the diagram draw an arrow showing the electric forceon the aluminum ball. Label the arrow−→Fel.(c) Calculate the magnitude of the electric force on the alu-minum ball due to the charged rod. Show your work.penmetal ball3 cm(d) What approximations, if any, did you make in your calculation?3Now the aluminum ball is removed and replaced by a solidplastic ball. The plastic ball is neutral and is held in place byan insulating string, which is not shown in the diagram.(e) On the diagram at right, clearly show the distribution ofcharge in and/or on the plastic ball.(f) On the diagram at right, draw an arrow showing the electricforce on the plastic ball. Label the arrow−→Fel.penplastic ball4015-004A plastic ballpoint pen of length 14 cm is rubbed all over withwool and acquires a charge of -3x10−8coulombs, distributedmore or less evenly over the surface of the pen. A solid alu-minum ball suspended from an insulated string is touched to aVan de Graaff generator and acquires a charge of -2x10−9C.The charged ball is brought near the pen, as shown in the dia-gram. (The ball is held in place by the insulating string, whichis not shown in the diagram). The center of the ball is 4 cmfrom the pen.(a) On the diagram at right, clearly show the distribution ofcharge in and/or on the aluminum ball.(b) On the diagram draw an arrow showing the electric forceon the aluminum ball. Label the arrow−→Fel.(c) Calculate the magnitude of the electric force on the alu-minum ball due to the charged rod. Show your work.penmetal ball4 cm(d) What approximations, if any, did you make in your calculation?5Now the aluminum ball is removed and replaced by a solidplastic ball. The plastic ball is neutral and is held in place byan insulating string, which is not shown in the diagram.(e) On the diagram at right, clearly show the distribution ofcharge in and/or on the plastic ball.(f) On the diagram at right, draw an arrow showing the electricforce on the plastic ball. Label the arrow−→Fel.penplastic ball6015-005A plastic ball of radius Rballis throroughly rubbed with wooland becomes uniformly charged with total charge −Q.Thecharged ball is placed above a small disk-shaped piece of alu-minum foil of radius Rfoiland thickness t,whereRfoilis muchless than Rballand t is much less than Rfoil(in the diagram,the thickness of the foil is greatly exaggerated to indicate somethickness). The center of the ball is a height h above the foil.(a) Show the distribution of charge on this expanded drawingof the aluminum foil:(b) Calculate algebraically the amount of charge q on the uppersurface of the aluminum foil in terms of the given quantities(Q, Rball,Rfoil,t,andh).(c) Given that the ball was thoroughly rubbed and therefore acquired as much charge as it could hold,calculate numerically in coulombs the charge q on the upper surface of the aluminum foil, given that theradius of the ball Rball= 5 mm; the radius of the foil Rfoil= 1 mm; the thickness of the foil t =0.01mm; the height of the center of the ball above the foil h = 2 cm; and the density ρ of aluminum is 2.7grams/cm3.7015-006A plastic ball of radius Rballis throroughly rubbed with wooland becomes uniformly charged with total charge −Q.Thecharged ball is placed above a small disk-shaped piece of alu-minum foil of radius Rfoiland thickness t,whereRfoilis muchless than Rballand t is much less than Rfoil(in the diagram,the thickness of the foil is greatly exaggerated to indicate somethickness). The center of the ball is a height h above the foil.(a) Show the distribution of charge on this expanded drawingof the aluminum foil:(b) Calculate algebraically the amount of charge q on the uppersurface of the aluminum foil in terms of the given quantities(Q, Rball,Rfoil,t,andh).(c) Given that the ball was thoroughly rubbed and therefore acquired as much charge as it could hold,calculate numerically in coulombs the charge q on the upper surface of the aluminum foil, given that theradius of the ball Rball= 5 mm; the radius of the foil Rfoil= 1 mm; the thickness of the foil t =0.01mm; the height of the center of the ball above the foil h = 2 cm; and the density ρ of aluminum is 2.7grams/cm3.(d) Very difficult! When the ball is moved down toward the aluminum foil, at a certain height thealuminum foil leaps upward. Estimate numerically this height in centimeters. The radius of the ball R =5


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SEWANEE PHYS 104 - Matter & Interactions 2d Edition

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