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BIO Signal Propagation in Neurons. Neurons are components of the nervous system of the body that transmit signals as electric impulses travel along their length. These impulses propagate when charge suddenly rushes into and then out of a part of the neuron called an axon. Measurements have shown that, during the inflow part of this cycle, approximately 5.6 × 10 11 Na+ (sodium ions) per meter, each with charge +e, enter the axon. How many coulombs of charge enter a 1.5-cm length of the axon during this process?
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- Assume a length of axon membrane of about 0.10 m is excited by an action potential (length excited = nerve speed pulse duration = 50.0 m/s 2.0 103 s = 0.10 m). In the resting state, the outer surface of the axon wall is charged positively with K+ ions and the inner wall has an equal and opposite charge of negative organic ions, as shown in Figure P18.43. Model the axon as a parallel-plate capacitor and take C = 0A/d and Q = C V to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 1.0 108 m, axon radius r = 1.0 101 m, and cell-wall dielectric constant = 3.0. (a) Calculate the positive charge on the outside of a 0.10-m piece of axon when it is not conducting an electric pulse. How many K+ ions are on the outside of the axon assuming an initial potential difference of 7.0 102 V? Is this a large charge per unit area? Hint: Calculate the charge per unit area in terms of electronic charge e per squared (2). An atom has a cross section of about 1 2 (1 = 1010 m). (b) How much positive charge must flow through the cell membrane to reach the excited state of + 3.0 102 V from the resting state of 7.0 102 V? How many sodium ions (Na+) is this? (c) If it takes 2.0 ms for the Na+ ions to enter the axon, what is the average current in the axon wall in this process? (d) How much energy does it take to raise the potential of the inner axon wall to + 3.0 102 V, starting from the resting potential of 7.0 102 V? Figure P18.43 Problem 43 and 44.arrow_forwardBy what factor is the capacitance of a metal sphere multiplied if its volume is tripled? (a) 3 (b) 31/3 (c) 1 (d) 31/3 (e) 13arrow_forwardWrite a question about the electrical action potential of the human nervous system in terms of physics.arrow_forward
- An electron in an x-ray machine is accelerated through a potential difference of 1.0 × 104 V before it hits the target. What is the kinetic energy of the electron in electron volts?arrow_forwardNerve cells transmitelectric signals through their long tubular axons. These signals propagatedue to a sudden rush of Na+ ions, each with charge +e, into theaxon. Measurements have revealed that typically about 5.6 * 10^11 Na+ions enter each meter of the axon during a time of 10 ms. What is thecurrent during this inflow of charge in a meter of axon?arrow_forwardYou are working in a laboratory, using very sensitive measurement equipment. Your supervisor has explained that the equipment is also very sensitive to electrical discharge from human operators. Specification tables for the equipment indicate that an electrical discharge providing even a very small amount of energy of 250 μJ is enough to damage the equipment. Your supervisor wants to install an apparatus that will be used to remove the electrical charge from individuals’ bodies before they touch the equipment. To do this, she asks you to estimate (a) the capacitance of the human body and determine (b) the charge on the body and (c) the electric potential of the body, relative to a point infinitely far away, corresponding to the energy transfer that will damage the equipment.arrow_forward
- An axon is the relatively long tail-like part of a neuron, or nerve cell. The outer surface of the axon membrane (dielectric constant = 5, thickness = 1 × 10^–8 m) is charged positively, and the inner portion is charged negatively. Thus, the membrane is a kind of capacitor. If the membrane acts like a parallel plate capacitor with a plate area of 5 × 10^–6 m^2, what is its capacitance?arrow_forwardIn Example 23.14 we estimated the capacitance of the cell membrane to be 89 pF, and in Example 23.15 we found that approximately 10,000 Na+ ions flow through an ion channel when it opens. Based on this information and what you learned about the action potential, estimate the total number of sodium channels in the membrane of a nerve cell.arrow_forwardSuppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rb has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = ae Trao + B/r + bo where alpha (a), beta (ß), ao and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference ab between the two conductors. The potential difference is related to the electric field by: Vob = - S *Edr= - ["Edr Calculating the antiderivative or indefinite integral, Vab = (-aage" o-r/ao + B + bo By definition, the capacitance C is related to the charge and potential difference by: C = Evaluating with the upper and lower limits of integration for Vab, then simplifying: C = Q/( (erb/ao - eralao) + ß In( ) + bo ( ))arrow_forward
- Part (a) Express the time constant τ in terms of R and C. τ = ______ Part (b) Calculate the numerical value of τ in μs. τ = ______ Part (c) Express the maximum charge Q on the capacitor in terms of C and ε. Q = ______ Part (d) Calculate the numerical value of Q in μC. Q = ______arrow_forwardThe voltage across a capacitor is given by the formula V=Q/C, where Q is usually called "the charge on the capacitor." Where is this charge in a capacitor? Does the capacitor really have a net charge?arrow_forwardA nerve signal is transmittedthrough a neuron when an excess of Na+ ions suddenly enters the axon,a long cylindrical part of the neuron. Axons are approximately 10.0 mmin diameter, and measurements show that about 5.6 * 1011 Na+ ions permeter (each of charge +e) enter during this process. Although the axonis a long cylinder, the charge does not all enter everywhere at the sametime. A plausible model would be a series of point charges moving alongthe axon. Consider a 0.10 mm length of the axon and model it as a pointcharge. (a) If the charge that enters each meter of the axon gets distributeduniformly along it, how many coulombs of charge enter a 0.10 mmlength of the axon? (b) What electric field (magnitude and direction)does the sudden influx of charge produce at the surface of the body ifthe axon is 5.00 cm below the skin? (c) Certain sharks can respond toelectric fields as weak as 1.0 mN/C. How far from this segment of axoncould a shark be and still detect its electric field?arrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning