Biology
1. A nerve signal is transmitted through a neuron when an excess of Na+ ions suddenly enters the axon, a long cylindrical part of the neuron. Axons are approximately 10.0 µm in diameter, and measurements show that about 5.6 x 1011 Na+ ions per meter (each of charge +e) enter during the process. Although the axon is a long cylinder, the charge does not all enter everywhere at the same time. A plausible model would be a series of nearly point charges moving along the axon. Let us look at a 0.10 mm length of the axon and model it as a point charge.
a. If the charge that enters each meter of the axon gets distributed uniformly along it, how many coulombs of charge enter a 0.10 mm length of the axon?
b. What electric field (magnitude and direction) does the sudden influx of charge produce at the surface of the body if the axon is 5.00 cm below the skin?
c. Certain sharks can respond to electric fields as weak as 1.0 µN/C. How far from this segment of axon could a shark be and still detect its electric field?

2. Neurons are the basic units of the nervous system. They contain axons. The axon contains a solution of potassium ions K+ and large negative ions. The axon membrane prevents the large ions from leaking out, but the smaller K+ ions are able to penetrate the membrane to some degree. This leaves an excess of negative charge on the inner surface of the axon membrane and an excess of positive charge on the outer surface, resulting in a potential difference across the membrane, which is typically about 70 mV. The thickness of the axon membrane itself varies from about 5 to 10 nm, so an average of 7.5 nm is a good approximation. We can model the membrane as a large sheet having equal and opposite charge densities on its faces.
a. Find the electric field inside the axon membrane, assuming (not too realistically) that it is filled with air. Which way does it point, into or out of the axon?
b. Which is at the highest potential, the inside surface or the outside surface of the axon membrane?
c. How the results obtained in parts (a) and (b) will change if we assume a more realistic model, where the membrane contains proteins embedded in an organic material to give the membrane a dielectric constant of about 10.
d. What is the capacitance per square centimeter of such a cell wall?

3. Communication in the nervous system is based on propagating electrical signals called action potentials that travel along the extended nerve cells, the axons. Action potentials are generated when the electrical potential difference across the membrane changes so that the inside of the cell becomes more positive. Researchers in clinical medicine and neurobiology want to stimulate nerves non-invasively at specific locations in conscious subjects. But using electrodes to apply current on the skin is painful and requires large currents. Anthony Barker and colleagues at the University of Sheffield in England developed a technique that is now widely used and it is called Transcranial Magnetic Stimulation (TMS). In the TMS technique, a coil positioned near the skull produces a time-varying magnetic field, which induces electric currents in the conductive brain tissue sufficient to cause action potentials in the nerve cells. For example, if the coil is placed near the motor cortex, the region of the brain that controls voluntary movements, scientists can monitor the contraction of the muscle and assess the state of the connections between the brain and the muscle.
In the accompanying diagram of the TMS a current pulse increases to a peak and then decreases to zero in the direction shown in the stimulating coil. What will be the direction (1 or 2) of the induced current in the brain tissue?
a. 1
b. 2
c. 1 while the current increases in the stimulating coil and 2 while the current decreases.
d. 2 while the current increases in the stimulating coil, 1 while the current decreases.
The brain tissue at the level of the dotted line may be considered as a series of concentric circles, with each circle behaving independently. Where will be the induced EMF is the greatest?
a. At the center of the dotted line.
b. At the periphery of the dotted line.
c. The EMF will be the same in all concentric circles.
d. At the center during the increasing phase of the stimulating current and at the periphery during the decreasing phase.
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