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Material Type: Assignment; Class: Mechanics; Subject: Physics; University: Lafayette College; Term: Spring 2009;
Typology: Assignments
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May 1, 2009
Physics 131 Level II Homework Set Section 1
You may discuss these problems with one or two other students (or with your instructor), but your final solutions should be written out by you alone. Under no circumstances should you see another student’s written solutions. If you have discussed these problems with anyone you must acknowledge the collaboration at the beginning of the corresponding problem. Homework is due in my office by 3:30 PM on the due date and solutions will then be made available on the course web site. No homework will be accepted after this time.
You are expected to carefully explain how, starting from basic principles, you have arrived at your answers. Please do not use paper with edges frayed from being ripped out of a spiral bound notebook. If the papers are illegible or disorganized, we reserve the right to return these papers without being graded. Unless instructed otherwise, all answers should be correct to 3 or 4 sig. figs.
Assignment 14: Due Wednesday, May 6, 2009
Problem 1 (60 pnts): Consider a simple model for the polar nature of H 2 0. Let the oxygen have exactly two excess electrons, placed at its center, and the hydrogen atoms be completely stripped of their electrons. Let the oxygen-hydrogen bond distance be D , and take the H-O-H bond angle to be 120° (it is not, but this makes the algebra a bit simpler). Place the oxygen ion on the negative x -axis, and place the hydrogen ions symmetrically on the y -axis (one below the origin and one above). The answers below will be in terms of ke , e , and D. Note that each part is worth 10 points.
A] Calculate the dipole moment of the molecule (be careful, this is a vector calculation). Think of this as the sum of two separate dipoles pointing in different directions.
B] Find the electric force on a proton placed along the x -axis as a function of x , for both x > 0 and x < − D.
C] Find the electric force on an electron placed on the y -axis as a function of y , for both y > D and y < − D.
D] Find the electric potential energy of the H 2 O molecule due to the separation of charge of the molecule.
E] Find the net electrostatic force on the upper hydrogen ion.
electron on the oxygen.