9.2.P39
| Signals travel down a nerve cell's axons by perturbing the electrical energy stored in the capacitance of the membrane. An axon is essentially a cylindrical capacitor – a long cylinder (the inner surface of the cell membrane) surrounded by a slightly larger one (the outer surface of the cell membrane with a potential difference of ΔV = 70 mV across it. To get an idea of the energetics involved, estimate the electric energy stored in the polarized membrane of a motor neuron. Model the membrane of the axon of a motor neuron as a capacitor. Ignore, for now, the contents of the membrane and the myelin sheath on the axon. The axon has a diameter of about 10 microns (μm), its membrane has a thickness of about 8 nanometers (nm), and a motor axon may be one meter long. To help you in building your model, the capacitance of a parallel plate capacitor of area A and plate separation d is C = A/(4πkC d) and the energy stored in it is E = ½ C ΔV 2. Be sure to clearly state your assumptions and how you came to the numbers you estimated, since grading on this problem will be mostly based on your reasoning, not on your answer. |  |
Joe Redish 4/21/17