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Problems

           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.)

Due 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.

 

Due November 14 ( solutions)
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.

* C14 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.