Homework Help is Here – Start Your Trial Now!
Science
Physics
Problem 1: A neuron is a body cell that functions to create and transmit electrical signals. To do this, it uses chemical processes to maintain an electrical potential difference across its cell membrane. In this problem we will use our knowledge of electrical relationships to estimate the amount of charge on the membrane. Neurons come in a range of sizes, but a typical one may have a cell body of 20 µm (2 x 10¹5 m) across. The thickness of the membrane is the same for most neurons - about 5 nm (5 x 10¹⁹ m). The potential difference across a resting nerve membrane is about 70 mV (70 x 10¹³ V). We'll model a piece of the cell membrane 10 µm x 10 µm across as a pair of infinite parallel plates separated by a distance d = 5 nm, with one plate representing the inner edge of the membrane and the other representing the outer edge of the membrane. A. Assuming the space separating the two plates of our membrane is empty space, calculate the electric field between the plates. B. Using the electric field you found in part A, calculate the charge density, o (charge per unit area), on the plates. (Hint: The E field near to a single plate of charge having a uniform charge density σ, is 2лko where kc = 9 x 10° N-m²/C².) C. Using the charge density you found in B, calculate the magnitude of the charge on each side of the piece of cell membrane we are modeling and the net charge on the piece of the membrane. D. Do you think our model of the electric fields and potentials in a cell membrane as infinite parallel plates is a good one? Give reasons for your judgment.

Problem 1: A neuron is a body cell that functions to create and transmit electrical signals. To do this, it uses chemical processes to maintain an electrical potential difference across its cell membrane. In this problem we will use our knowledge of electrical relationships to estimate the amount of charge on the membrane. Neurons come in a range of sizes, but a typical one may have a cell body of 20 µm (2 x 10¹5 m) across. The thickness of the membrane is the same for most neurons - about 5 nm (5 x 10¹⁹ m). The potential difference across a resting nerve membrane is about 70 mV (70 x 10¹³ V). We'll model a piece of the cell membrane 10 µm x 10 µm across as a pair of infinite parallel plates separated by a distance d = 5 nm, with one plate representing the inner edge of the membrane and the other representing the outer edge of the membrane. A. Assuming the space separating the two plates of our membrane is empty space, calculate the electric field between the plates. B. Using the electric field you found in part A, calculate the charge density, o (charge per unit area), on the plates. (Hint: The E field near to a single plate of charge having a uniform charge density σ, is 2лko where kc = 9 x 10° N-m²/C².) C. Using the charge density you found in B, calculate the magnitude of the charge on each side of the piece of cell membrane we are modeling and the net charge on the piece of the membrane. D. Do you think our model of the electric fields and potentials in a cell membrane as infinite parallel plates is a good one? Give reasons for your judgment.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
See similar textbooks
icon
Related questions
Question
Problem 1: A neuron is a body cell that functions to create and transmit electrical signals. To do this, it uses chemical processes to maintain an electrical potential difference across its cell membrane. In this problem we will use our knowledge of electrical relationships to estimate the amount of charge on the membrane. Neurons come in a range of sizes, but a typical one may have a cell body of 20 µm (2 x 105 m) across. The thickness of the membrane is the same for most neurons - about 5 nm (5 x 10⁹ m). The potential difference across a resting nerve membrane is about 70 mV (70 x 10-³ V). We'll model a piece of the cell membrane 10 µm x 10 µm across as a pair of infinite parallel plates separated by a distance = = 5 nm, with one plate representing the inner edge of the membrane and the other representing the outer edge of the membrane. A. Assuming the space separating the two plates of our membrane is empty space, calculate the electric field between the plates. B. Using the electric field you found in part A, calculate the charge density, o (charge per unit area), on the plates. (Hint: The E field near to a single plate of charge having a uniform charge density o, is 2лkco where kc = 9 x 10° N-m²/C².) C. Using the charge density you found in B, calculate the magnitude of the charge on each side of the piece of cell membrane we are modeling and the net charge on the piece of the membrane. D. Do you think our model of the electric fields and potentials in a cell membrane as infinite parallel plates is a good one? Give reasons for your judgment.
Transcribed Image Text:Problem 1: A neuron is a body cell that functions to create and transmit electrical signals. To do this, it uses chemical processes to maintain an electrical potential difference across its cell membrane. In this problem we will use our knowledge of electrical relationships to estimate the amount of charge on the membrane. Neurons come in a range of sizes, but a typical one may have a cell body of 20 µm (2 x 105 m) across. The thickness of the membrane is the same for most neurons - about 5 nm (5 x 10⁹ m). The potential difference across a resting nerve membrane is about 70 mV (70 x 10-³ V). We'll model a piece of the cell membrane 10 µm x 10 µm across as a pair of infinite parallel plates separated by a distance = = 5 nm, with one plate representing the inner edge of the membrane and the other representing the outer edge of the membrane. A. Assuming the space separating the two plates of our membrane is empty space, calculate the electric field between the plates. B. Using the electric field you found in part A, calculate the charge density, o (charge per unit area), on the plates. (Hint: The E field near to a single plate of charge having a uniform charge density o, is 2лkco where kc = 9 x 10° N-m²/C².) C. Using the charge density you found in B, calculate the magnitude of the charge on each side of the piece of cell membrane we are modeling and the net charge on the piece of the membrane. D. Do you think our model of the electric fields and potentials in a cell membrane as infinite parallel plates is a good one? Give reasons for your judgment.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Electric field
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON
SEE MORE TEXTBOOKS