Lafayette College
Department of Physics
May 1, 2009
Physics 131 LevelIIHomework Set Section 1
Youmay discuss these problems with one or twoother students (or with your instructor), but
your final solutions should be written out by you alone. Under no circumstances should you see
another student’swritten 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.
Youare expected to carefully explain how, starting from basic principles, you have arrivedat
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 reservethe 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 H20. Let the oxygen
have exactly twoexcess electrons, placed at its center,and the hydrogen atoms be completely
stripped of their electrons. Let the oxygen-hydrogen bond distance be D,and takethe H-O-H
bond angle to be 12 0°(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 belowthe
origin and one above). The answers belowwill 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 twoseparate 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>Dand y<−D.
D] Find the electric potential energy of the H2Omolecule due to the separation of charge
of the molecule.
E] Find the net electrostatic force on the upper hydrogen ion.
F] Find the electrostatic work required to remove one hydrogen ion to ∞,leaving it’s
electron on the oxygen.