General Physics, 2nd Edition
2nd Edition
ISBN: 9780471522782
Author: Morton M. Sternheim
Publisher: WILEY
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Chapter 18, Problem 7E
(a)
To determine
The direction and magnitude of the electric field in the membrane.
(b)
To determine
The value of dielectric constant.
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In a typical mammalian cell, the net transport by the sodiumpotassium exchange pump that maintains the 70 mV membrane potential is 500 singly charged ions per second. How much work does the pump do each second?
The giant axon of a squid is 0.5 mm in diameter, 10 cm long, and not myelinated. Unmyelinated cell membranes behave as capacitors with 1 μF of capacitance per square centimeter of membrane area. When the axon is charged to the -70 mV resting potential, what is the energy stored in this capacitance?
In 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.
Chapter 18 Solutions
General Physics, 2nd Edition
Ch. 18 - Prob. 1RQCh. 18 - Prob. 2RQCh. 18 - Prob. 3RQCh. 18 - Prob. 4RQCh. 18 - Prob. 5RQCh. 18 - Prob. 6RQCh. 18 - Prob. 7RQCh. 18 - Prob. 8RQCh. 18 - Prob. 9RQCh. 18 - Prob. 10RQ
Ch. 18 - Prob. 1ECh. 18 - Prob. 2ECh. 18 - Prob. 3ECh. 18 - Prob. 4ECh. 18 - Prob. 5ECh. 18 - Prob. 6ECh. 18 - Prob. 7ECh. 18 - Prob. 8ECh. 18 - Prob. 9ECh. 18 - Prob. 10ECh. 18 - Prob. 11ECh. 18 - Prob. 12ECh. 18 - Prob. 13ECh. 18 - Prob. 14ECh. 18 - Prob. 15ECh. 18 - Prob. 16ECh. 18 - Prob. 17ECh. 18 - Prob. 18ECh. 18 - Prob. 20ECh. 18 - Prob. 21ECh. 18 - Prob. 24ECh. 18 - Prob. 25ECh. 18 - Prob. 26E
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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_forwardAccording to UE=12C(V)2 (Eq. 27.3), a greater capacitance means more energy is stored by the capacitor, but according to UE = Q2/2C (Eq. 27.2), a greater capacitance means less energy is stored. How can both of these equations be correct?arrow_forwardA capacitor is made up of two long coaxial cylindrical conductorsseparated by a vaccum. If the capacitance per unit length is 97.0 pF/m,the ratio of the radii of the outer cylinder and the inner cylinder is mostnearlyarrow_forward
- Find the relative permittivity εr of the dielectric material present in a parallel-plate capacitor if:A = 0.12 m2, d = 80 µm, V =12 V, U =1 µJarrow_forwardCompute for the capacitance of a sphere (C= 4πer) if its radius is 5 cm and the dielectric material used is mica, relative permittivity is 6.0.arrow_forwardIf the capacitance is 47μF, and the voltage difference across the capacitor terminals is 6V, then the charge stored in that capacitor is:arrow_forward
- Calculate the capacitance of the myelinated neuron membrane (axon), if its thickness is 0.8 micrometres (um) using a value of area of 10-6 m2. The membrane wall is mainly lipids and you will need to find the value of the permittivity in your notes. Give your answer in picoFarads (10-12 F) NB 1um = 10-6 marrow_forwarda potential difference of V = 85.1 V is applied across a capacitor arrangement with capacitances C1 = 10.3 μF, C2 = 5.37 μF, and C3 = 3.75 μF. If capacitor 3 undergoes electrical breakdown so that it becomes equivalent to conducting wire, what is the increase in (a) the charge on capacitor 1 and (b) the potential difference across capacitor 1?arrow_forwardPlease help. The nonpolar core of the membrane of a muscle cell has a thickness d = 4nm and a dielectric constancy k = 20. (a) What is the surface capacity of the membrane? Express your response in microcoulombs per square centimeter. (b) During muscle contraction, the internal potential of the cell increases by about 100 mV. For 1 cm2 of membrane, how many Na+ ions must have entered the cell for this purpose? (c) The medium outside the cell initially contains 0.150 mol / L of Na + ions in solution. Considering that it extends to 1 µm from the cell, what is the decrease in Na+ concentration immediately after the change in potential? (d) Estimate the number of times the process can be repeated before the Na+ ion reserve is exhausted. Please show formulas ans steps for my own understandingarrow_forward
- A cylindrical capacitor consists of a solid inner conducting core with radius 0.250 cm, surrounded by an outer hollow conducting tube. The two conductors are separated by air, and the length of the cylinder is 15.0 cm. The capacitance is 34.2 pF. ) If the capacitor is charged to 250V, what will be the charge per unit length?arrow_forwardAn axon is the relatively long tail-like part of a neuron. The outer surface ofthe axon membrane (dielectric constant = 5, thickness = 1 x10 -8 m) ischarged positively, and the inner portion is charged negatively. Thus, themembrane is a kind of capacitor. Assuming that an axon can be treatedlike a parallel plate capacitor with a plate area of 5 x 10 -6 m 2 , what is itscapacitance?arrow_forwardFind the relative permittivity of the dielectric material present in a parallel-plate capacitor if: A = 0.12 m^2, d = 80 μm, V =12 V, U =1 μJarrow_forward
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