College Physics
1st Edition
ISBN: 9781938168000
Author: Paul Peter Urone, Roger Hinrichs
Publisher: OpenStax College
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Textbook Question
Chapter 20, Problem 32CQ
Explain the properties of myelinated nerves in terms of the insulating properties of myelin.
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Item 13
Cell Membranes and Dielectrics Many cells in the body have a cell
membrane whose inner and outer surfaces carry opposite charges, just like
the plates of a parallel-plate capacitor. Suppose a typical cell membrane has
a thickness of 8.5x109 m, and its inner and outer surfaces carry charge
densities of -6.4×10-4 C/m² and +6.4×10-4 C/m², respectively. In
addition, assume that the material in the cell membrane has a dielectric
constant of 5.4.
Part A
Find the direction of the electric field within the cell membrane.
into the cell
O out of the cell
Submit
Part B
E =
Find the magnitude of the electric field within the cell membrane.
Express your answer using two significant figures.
—| ΑΣΦ
Submit
Part C
Request Answer
|AV| =
Submit
Request Answer
Calculate the potential difference between the inner and outer walls of the membrane.
Express your answer using two significant figures.
17 ΑΣΦ
# ?
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N/C
?
mV
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 × 0.0020 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 the figure below. Model the axon as a parallel-plate capacitor and take C = ke,A/d and Q = CAV to investigate the charge as follows. Use
typical values for a cylindrical axon of cell wall thickness d = 1.4 x 10-8 m, axon radius r = 1.4 x 101 um, and cell-wall dielectric constant k = 2.2.
Chapter 20 Solutions
College Physics
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- A myelinated axon conducts nerve impulses at a speed of 40 m/s. What is the signal speed if the thickness of the myelin sheath is halved but no other changes are made to the axon?arrow_forward-gauge copper wire has a diameter of 9.266 mm. Calculate the power loss in a kilometer of such wire when it carries 1.00102 A.arrow_forwardAssume 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_forward
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