Exams for Matter Interactions II Electric Magnetic Interactions Here are three exams plus the final exam given in the electricity and magnetism course in Spring 2001 The three exams are hour exams in the sense that they are of a length typical of hour exams in other courses However we scheduled these exams in two hour blocks in the evening to permit students to take as much as an additional hour if desired to make sure there was no time pressure This results in more thoughtful work by the students and a better measure of their true capabilities The final exam was nominally a three hour exam but we gave students an extra hour if desired At the time that these exams were given in Spring 2001 these problems were not in the preliminary version of the textbook but many were added to the textbook before final publication 33 132 Exam 1 Thursday 2001 Feb 15 Name Read all problems carefully before attempting to solve them Your work must be legible and the organization must be clear Correct answers without adequate explanation will be counted wrong Incorrect explanations mixed in with correct explanations will be counted wrong Make explanations complete but brief Do not write a lot of prose Include diagrams 3 6 4 8 10 5 10 Show what goes into a calculation not just the final number 5 10 5 4 2 10 4 10 Give physical units with your results If you cannot do some portion of a problem invent a symbol for the quantity you can t calculate explain that you re doing this and do the rest of the problem Problem Score 1 33 pts 2 33 pts 3 34 pts 4 3 pts Total 100 pts Continued on next page Problem 1 33 pts A Van de Graaff generator pulls electrons out of the Earth and transports them on a conveyor belt onto a nearly spherical metal shell The diameter of this generator s metal shell is 30 cm To ground a 9 pts The conveyor belt in the Van de Graaff generator is running so fast that the generator succeeds in building up and maintaining just enough charge on the metal shell to cause the air to steadily glow bluish near the surface of the shell Under these conditions how much net charge Q is on the metal shell Calculate a numerical value for Q and explain briefly b 15 pts Now assume that the Van de Graaff generator is run more slowly and the buildup of charge on the metal shell is limited by the inability of the motor to force any more electrons onto the negatively charged shell The air no longer glows We have a pear shaped piece of metal that is attached by a metal wire to the earth grounded When we bring the grounded piece of metal to a location near the Van de Graaff metal shell we observe a big spark Explain in detail why a spark occurs now but doesn t occur without the additional piece of metal nearby 30 cm 30 cm c 9 pts The spark lasts only a very short time Why Explain in detail Problem 2 33 pts Consider a thin plastic rod bent into a semicircular arc of radius R with center at the origin The rod carries a uniformly distributed negative charge Q a 28 pts Determine the electric field E at the origin contributed by the rod Include carefully labeled diagrams and be sure to check your result y Q R x b 5 pts An ion with charge 2e and mass M is placed at rest at the origin After a very short time t the ion has moved only a very short distance but has acquired some momentum p Calculate p Problem 3 34 pts A thin spherical shell of radius R1 made of plastic carries a uniformly distributed negative charge Q1 A thin spherical shell of radius R2 made of glass carries a uniformly distributed positive charge Q2 The distance between centers is L Plastic Q1 Glass R1 Q2 R2 a 11 pts Find the potential difference VB VA Location A is at the center of the glass sphere and location B is just outside the glass sphere A C B d L b 12 pts Find the potential difference VC VB Location B is just outside the glass sphere and location C is a distance d to the right of B c 11 pts Suppose the glass shell is replaced by a solid metal sphere with radius R2 carrying charge Q2 Would the magnitude of the potential difference VB VA be greater than less than or the same as they were with the glass shell in place Explain briefly including an appropriate physics diagram Plastic Q1 Metal R1 Q2 R2 A C B d L Problem 4 3 pt bonus question If you get a total score greater than 100 we round down to 100 Since this problem is only worth 3 bonus points don t attempt it unless you have finished all the other problems and checked your work Here is a pattern of electric field in which the electric field is horizontal throughout this region but is larger toward the top of the region and smaller toward the bottom If this pattern of electric field can be produced by some arrangement of stationary charges sketch such a distribution of charges If this pattern of electric field cannot be produced by any arrangement of stationary charges prove that it is impossible Fundamental Concepts 1 q E r 4 0 r 2 U el V q dP total F net dt F2 q2E1 f i dV E x dx V V f V i E dl U el qV Specific results and data Q 1 1 2 Q L E rod a perpendicular distance r from the center E rod if r L r 4 0 r r 2 L 2 2 4 0 1 qz E ring a distance z along the axis 4 0 z 2 R 2 3 2 1 Q E solid sphere r inside solid sphere of radius R 4 0 R 3 Q A Q A Q A z z E disk 1 a distance z along the axis E disk 1 if z R 1 2 2 2 2e 0 2 0 2e R z R 0 Q A Q A s E capacitor for Q and Q disks E fringe just outside capacitor 0 0 2R 1 2qs 1 qs along perpendicular axis where y s E dipole x along axis where x s E x 4 0 x 3 4 0 y 3 1 2 Q 2 F for point charge acting on a neutral atom 4 0 r 5 1 q V point charge 4 0 r p qs E E E inside an insulator K Physical constants N m 21 9 109 4 0 C2 0 9 10 27 mproton mneutron mhydrogen atom 1 7 10 e 1 6 10 27 mproton mneutron mhydrogen atom 1 7 10 23 molecules mole 31 19 c 3 10 m s 6 10 C2 N m 2 …