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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Assume a length of axon membrane of about 0.10 m is excited by an action potential (length excited = nerve speed x pulse duration = 50.0 m/s x 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 = K² A/d and Q = CAV to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 2.0 x 10-8 m, axon
radius r = 1.6 x 10¹ μm, and cell-wall dielectric constant k = 2.9.
Positive
charge
layer
Negative
charge
layer
External fluid
Axon wall membrane
Internal fluid
- Axon radius=
d
-2
(a) Calculate the positive charge on the outside of a 0.10-m piece of axon when it is not conducting an electric pulse. (Assume an initial potential difference of 7.0 x 10-² v.)
9.03E-10
C
How many K+ ions are on the outside of the axon assuming an…
Assume a length of axon membrane of about 0.10 m is excited by an action potential (length excited = nerve speed x pulse duration = 50.0 m/s x 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 =
2.0 × 10-8 m, axon
radius r = 1.6 × 10¹ µm, and cell-wall dielectric constant x = 2.9.
Positive
charge
layer
Negative
charge
layer
External fluid
Axon wall membrane
Internal fluid
Axon radius = r
No
+
(a) Calculate the positive charge on the outside of a 0.10-m piece of axon when it is not conducting an electric pulse. (Assume an initial potential difference of 7.0 x 10-² v.)
d
Your response differs significantly from the correct answer. Rework your…
Assume a length of axon membrane of about 0.10 m is excited by an action potential (length excited = nerve speed x pulse duration = 50.0 m/s x 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 = 1.3 x 10-8
m, axon radius r = 1.3 × 10¹ μm, and cell-wall dielectric constant x = 2.1.
Positive
charge
layer
Negative
charge
layer
External fluid
+
Axon wall membrane
Internal fluid
Axon radius = r
+
+
How many sodium ions (Na+) is this?
Na+ ions
+
(a) Calculate the positive charge on the outside of a 0.10-m piece of axon when it is not conducting an electric pulse. (Assume an initial potential difference of 7.0 x 10-² V.)
C
How many K+ ions are on…
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_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 × 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 = ??0A/d and Q = CΔV to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 1.1 ✕ 10−8 m, axon radius r = 2.0 ✕ 101 ?m, and cell-wall dielectric constant ? = 2.7. A diagram shows a collection of positive and negative charges in and around an axon. The diagram is divided into three sections, one on top of the other. The top section is labeled "External fluid". A row of positive charges labeled "Positive charge layer" lies along the bottom side of this section. Above the row of positive charges, there is an even mixture of…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 × 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 = ??0A/d and Q = CΔV to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 1.6 ✕ 10−8 m, axon radius r = 1.9 ✕ 101 ?m, and cell-wall dielectric constant ? = 2.6. (a) Calculate the positive charge on the outside of a 0.10-m piece of axon when it is not conducting an electric pulse. (Assume an initial potential difference of 7.0 ✕ 10−2 V.)?CHow many K+ ions are on the outside of the axon assuming an initial potential difference of 7.0 ✕ 10−2 V??K+ ions (b) How much positive charge must flow through the cell membrane to reach…arrow_forward
- 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.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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- Cylindrical-conductors has inner and outer radii of 2 mm and 50 mm, respectively. If V(p = 2 mm) = 150 V and V(p = 50 mm) = 0 V, &r 10, dielectric conductivity 5x10-4 s/m, the dielectric resistance equals to 803.96 2 1024.59 2 1153.66 Q 1245.23 2arrow_forwardCylindrical-conductors has inner and outer radii of 2 mm and 100 mm, respectively. If V(p = 2 mm) = 150 V and V(p = 100 mm) = 0 V, Ɛr = 10, %3D dielectric conductivity 5x10-4 s/m, the dielectric resistance equals to 803.96 2 1024.59 2 1153.66 2 1245.23 2arrow_forwardIf the current travels before most of it have leakage out through membrane for unmyelinated axon is = 0.08 cm, then the radius of the axon is: (Rm = 0.2 2.m², pa = 2 N.m and Cm = 10° F.m*) 5 um 12.8 um O 12 um 1.8 um 3.2 umarrow_forward
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