Here are the assigned problems.
The problem solving handout gives
specific instructions on how to solve these problems (as well
as others you may encounter in other coruses or later in life).
Dr. Jeff's solutions can be found by clicking on the document
icons. (Remember, these are not necessarily the only solutions;
other assumptions and model may produce in different results.
Of course, not all models and assumptions are equally valid. Your
solution must match the given information and general physical
behavior of the world.)
Due Sept 10 ( solutions)
You are spending the summer working for a chemical company. Your
boss has asked you to determine where a chlorine ion of effective
charge -e would situate itself near a carbon dioxide ion. The
carbon dioxide ion is composed of 2 oxygen ions each with an effective
charge -2e and a carbon ion with an effective charge +3e. These
ions are arranged in a line with the carbon ion sandwiched midway
between the two oxygen ions. The distance between each oxygen
ion and the carbon ion is 3.0 x 10-11 m. Assuming that the chlorine
ion is on a line that is perpendicular to the axis of the carbon
dioxide ion and that the line goes through the carbon ion, what
is the equilibrium distance for the chlorine ion relative to the
carbon ion on this line? For simplicity, you assume that the carbon
dioxide ion does not deform in the presence of the chlorine ion.
You've been hired to
design the hardware for an ink-jet printer. You know that these
printers use an electrode to deflect the droplets, causing them
to form letters on a page. The basic mechanism is that uniform
ink drops of about 2x10-6m radius are charged to varying
amounts after being sprayed out towards the page at a speed of
about 15 m/s. Along the way to the page, they pass into a region
between two deflecting plates that are 1.5 cm long. The deflecting
plates are 1.0 mm apart and produce a uniform electric field between
them of 1.5 x 106 N/C. You measure the distance from
the edge of the plates to the paper and find that it is one-half
inch. Assuming an uncharged droplet forms the bottom of the letter,
how much charge is needed on the droplet to form the top of a
letter (standard 12 point font).
Due Oct 5 ( solutions)
You have a great summer job in a research laboratory with a group
investigating the possibility of producing power from fusion.
The device being designed confines a hot gas of positively charged
ions, called plasma, in a very long cylinder with a radius of
2.0 cm. The charge density of the plasma in the cylinder is 6.0
x 10-5 C/m3. Positively charged tritium
ions are to be injected into the plasma perpendicular to the axis
of the cylinder in a direction toward the center of the cylinder.
Your job is to determine the speed that a tritium ion should have
when it enters the plasma cylinder so that its velocity is zero
when it reaches the axis of the cylinder. Tritium is an isotope
of hydrogen with one proton and two neutrons.
As you so often do,
you find yourself reflecting on past physics discussions, trying
to make sense of them in light of your new knowledge. (You do
this, right?!?!) The physics demo that is in your mind today is
the one that we did a few weeks ago which had a charged balloon
“picking up” small pieces of paper. The balloon, which
is a typical one of radius ~10cm, was rubbed on hair, then brought
near the pieces. When the balloon got within 10cm of the pieces,
they jumped up to the balloon. You decide to apply what you now
know about electric fields to this situation and determine the
amount of charge on the balloon. You estimate that the pieces
of paper where about 3mm in radius and 0.1mm thick (typical office
20lb paper). (Alternatively,… you perform the same experiment
with pieces of aluminum foil, 1mm radius and 0.01mm thick, and
see that the same balloon only needs to be 20cm away from the
foil pieces before they jump.)
Oct 26 ( solutions)
After impressing your research supervisor with your analysis of
electrical phenomena of neurons, she asks you to analyze electric
eels. The obvious question is- how do they stun or kill fish without
stunning or killing itself? She tells you that the eels generate
current with electroplaques, biological cells that are essentially
batteries, with an emf source and resistance. Each eel has approximately
140 rows of these cells that run the length of their body. Each
row contains nearly 5000 electroplaques. In your reading, you
learn that each electroplaque has an emf of 0.15V and a resistance
of 0.25Ω. After researching the conductivity of water as
well as fish, you decide to estimate the resistance of the water
(and fish) between the eel's head and tail to be 800Ω.
For a summer internship, you are finishing up your design of a
desk-top sized magnetic spectrometer for the purpose of measuring
the ratio of C12 to C14 atoms in a sample
in order to determine its age.* The idea is to develop
an apparatus that is sufficiently portable that it could be taken
into the field for measurements. Your initial design is
much like the spectrometer shown in figure 29-24; although, yours
does not have the velocity selector. The plan is that by
burning (vaporizing) a sample you will create a gas of carbon
atoms. These atoms will then pass through an “ionizer”
that, on average, strips one electron from each atom. By
putting the ions through an electrostatic accelerator- two capacitor
plates with small holes that permit the ions to enter and leave,
these ions are accelerated. The two plates are charged so
that they are at a voltage difference of 1000 volts. From
here, the ions enter a nearly constant, vertical magnetic field.
Your magnetic field needs to be adjusted to have the C12
and C14 ions separated by at least 2mm when they strike
the detector array.
is a radioactive isotope of carbon that behaves chemically almost
identically to its more common but slightly lighter sibling, C12
. The amount of C14 in the atmosphere stays about
constant since it is being produced continually by cosmic rays.
Once carbon from the air is bound into an organic substance, the
C14 will decay with half of them vanishing every 5730
years. The ratio of C14 to C12 in
an organic substance therefore tells how long ago it died.
You want to construct
an electromagnet by wrapping wire around a hollow plastic tube
(20cm long and 3cm in diameter), then connecting the wire to a
power supply. The goal is to have an interior field strength of
that has an interior field strength of 0.005 T. Due to other constraints,
the coil has to be wound as a single layer of wire. You have two
spools of wire from which to choose. #18 wire has a diameter of
about 1.02 mm and can carry a current of 6.0A before overheating.
#26 wire has a diameter of 0.41mm and can carry up to 1.0A.