Question

An axon is a long, slender projection of a nerve cell, or neuron e , that typically conducts electrical impulses e away from the neuron's cell body e . Capacitance (C) is the ability of a system to store an electric charge. In this activity, you'll use information given about these fascinating structures to calculate the capacitance of an axon. Αxon Axon terminal Dendrite Node of Ranvier Soma Axon Schwann cell Myelin sheath Nucleus plasma membrane cytoplasm, a conducting liquid axon or dendrite of a nerve cell Axons come in a wide variety of sizes, for example the length may vary from 1 mm up to 1 meter! We will model the axor a cylinder with given inner and outer radi. Suppose that we have an axon that is 10 cm long, with an inner radius r1 of 1 um and outer radius r2 = r1+ 1nm 1 um+ 1nm. In this exercise, you may use a dielectric constant for cellular fluid of K 3. 1. Write an expression for the magnitude of the Electric Field,"E" outside (at an arbitrary radius r) for a uniformly charged cylinder of length "I" with charge q": 1 Write an expression for the magnitude of the Electric Field, "E" outside (at an arbitrary radius r) for a uniformly charged cylinder of length "I" with charge "q": 2. This cylinder is in a dielectric fluid, not vacuum conditions (a conducting liquid lies between the inner and outer radii of the cylinder). How does that change your expression for E with a dielectric constant K? (This expression is in your textbook). Don't plug in any numbers yet. just give the expression 3. Make sure you understand how the concepts of electric field and potential difference (V) are related. If you need help, ask your recitation leader. Calculate the potential difference for a cylindrical capacitor of outer radius r2 and inner radius r1 and length I. Don't plug in any numbers yet. just give the expression. Hint: Try it on your own for practice, and if you need more help follow example 26.11 from your textbook "A cylindrical capacitor". Note: Your expression for V will differ from the one in the book very slightly due to the dielectric medium. Make sure you use your expression from (2.) for the electric field here, which includes the given dielectric constant. 4. What is the relationship between capacitance (C) and the potential difference (V) for a capacitor? Using this relationship, write down the capacitance for the axon in this activity.Give the expression, and then plug in the given values to get your answer in SI units

Answer 1

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