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Cell membranes. Cell membranes (the walled enclosure around a cell) are typically about 7.5 nm thick. They are partially permeable to allow charged material to pass in and out, as needed. Equal but opposite charge densities build up on the inside and outside faces of such a membrane, and these charges prevent additional charges from passing through the cell wall. We can model a cell membrane as a parallel-plate capacitor, with the membrane itself containing proteins embedded in an organic material to give the membrane a dielectric constant of about $10 .$ (See Figure $18.52 . )$ (a) Whatis the capacitance per square centimeter of such a cell wall? (b) In its normal resting state, a cell has a potential difference of 85 $\mathrm{mV}$ across its membrane. What is the electric field inside this membrane?

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Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 18

Electric Potential and Capacitanc

Kinetic Energy

Potential Energy

Energy Conservation

Electric Charge and Electric Field

Gauss's Law

Electric Potential

Capacitance and Dielectrics

Cornell University

Hope College

University of Winnipeg

Lectures

13:02

In physics, potential energy is the energy possessed by a body or a system due to its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units (SI) is the joule (J). One joule is the energy expended (or work done) in applying a force of one newton through a distance of one metre (1 newton metre). The term potential energy was introduced by the 19th century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concepts of potentiality. Potential energy is associated with forces that act on a body in a way that the work done by these forces on the body depends only on the initial and final positions of the body, and not on the specific path between them. These forces, that are called potential forces, can be represented at every point in space by vectors expressed as gradients of a scalar function called potential. Potential energy is the energy of an object. It is the energy by virtue of a position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force that works against the force field of the potential. This work is stored in the field, which is said to be stored as potential energy.

18:38

In physics, electric flux is a measure of the quantity of electric charge passing through a surface. It is used in the study of electromagnetic radiation. The SI unit of electric flux is the weber (symbol: Wb). The electric flux through a surface is calculated by dividing the electric charge passing through the surface by the area of the surface, and multiplying by the permittivity of free space (the permittivity of vacuum is used in the case of a vacuum). The electric flux through a closed surface is zero, by Gauss's law.

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Cell membranes. Cell membr…

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Cell membranes (the walled…

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BIO Cell Membranes. Cell m…

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B10 Cell Membranes. Cell m…

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24.52. Cell Membranes. Cel…

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Cell Membranes and Dielect…

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B1O Cell Membranes and Die…

(a) Calculate the capacita…

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The capacitance of biologi…

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The membrane that surround…

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06:39

So this problem is about how cell membranes could be modeled. His capacitors basically with di electrics inserted. So here's our capacitor or a cell membrane. And let's go ahead and get down some of the givens in the problem. So it says that the membranes are a seven and 1/2 nanometers thick, so we can say D is 7.5 times 10 to the minus nine meters. Okay. And we also know that the dye electric constant is 10. So cafa is equal to 10. And first we want to get the capacitance per square centimetre of the wall. So we want to use capacitance is equal to Absalon. Not a overdue. You let me just double check the room, actually modeling it as a parallel plate. Yeah, Parallel plate capacitor. Okay, great. So that's up. Absolutely not a divided by D. So? So the sea Per eh Um oh, we need to be concerned with units. So this But if we use s i units for capacitance and, uh absolutely not area D. This is gonna be in units of, um Oh, what are the units of capacitance? Let me double check that. Well, regardless, the area will be in units of meters squared, so it'll be whatever. The units of capacitance are divided by meters squared, so we need to convert that to centimeters squared. So we can do that. We'll need to multiply our answer by ah 100 centimeters or excuse me. We go back. You know what? I'm just gonna rewind a little bit. I think I've kind of gotten down a confusion whole. So I'm just going to calculate Seper a and then I'm gonna convert it. I think to me make it a little bit less confusing. So that's just gonna be absolutely not divided by D. And so I'm gonna go ahead and Oh, and then we also need Kappa. So, um and this is just a general formula that you can multiply by Kapo. So I'm gonna go ahead and plug that into a calculator. It crane 85 times. 10 to the minus 12. Kappa rose 10 and then D is seven and 1/2 nanometers. Seven points, Right. First time from light. It's night. Great. And so I got there. The capacitance per unit area is 0.118 Well, capacitance units is fair and I don't know where I forgot that. It's kind of funny. I've been writing it all day, but I blanked 0.118 fads per meter squared, and we want to get that two centimeters squared. So there was 100 centimeters in one meter, and then we have to go out twice. Multiply that twice to get, uh, you can get rid of the meter squared and converted two centimeters squared. So let's see. It's it's gonna be divided by 10 to the minus for so when So 10 to the minus four. Right now it's already 10 to the minus two. So then that will be 1.18 times 10 to the minus six fare ads per centimeter squared. Great. And next, we want to get the electric field inside the membrane. So we given that it has an 85 mobile voltage. So this is the answer for a So be we know V is equal toe 85 Mila Bolds. What is E? So I guess there's a few ways toe Answer this, um see, well, he is equal to deem my derivative of the with respect toe acts. So, uh, the magnitude of e could be said to be Delta bi over a delta eggs. So our delta acts is just the distance. So Alcoa had it right distance here on DSO. We just wanted to buy this 85. Miller holds by 7.5 on the animators. I'm gonna go ahead and do that eight point pry Brady of Fire 85 millet balls. Try to buy some one point front minus nine, huh? It's very small. I'm smarter than the wavelength of light. Wow, that seems really big, I guess because the distance is so small. I'm just gonna double check that. This was question was copied over, right? Because these numbers don't seem realistic to me, So I'll go ahead and pause the video while I do that. Hey, I double check the question. It really is Nana meters. So this tells us that the my calculation tells us that the electric field is, um, 11 million volts per meter. That seems crazy. 11 times 10 to the minus are tied to a plus six volts per meter. 88 5 seven in a hot Yeah,

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