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
10th Edition
ISBN:9781285737027
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter16: Electrical Energy And Capacitance
Section: Chapter Questions
Problem 35P: a parallel-plate capacitor with area 0.200 m2 and plate separation of 3.00 mm is connected to a...
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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.
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