How Is the Capacitance of an Axon Modeled as a Capacitor Calculated?

In summary, the outer surface of an axon is positively charged while the inner portion is negatively charged, making it act as a capacitor. Using the equation C = k * Eo * A / d, with a dielectric constant of 5, plate area of 4.20 * 10^-6 m^2, and thickness of 1 * 10^-8 m, the calculated capacitance is 1.9 * 10^-8 F, potentially incorrect due to rounding or incorrect units.
  • #1
themrk
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Homework Statement


An axon is the relatively long tail-like part of a neuron, or nerve cell. The outer surface of the axon membrane (dielectric constant = 5, thickness = 1 10-8 m) is charged positively, and the inner portion is charged negatively. Thus, the membrane is a kind of capacitor. Assuming that an axon can be treated like a parallel plate capacitor with a plate area of 4.20 10-6 m2, what is its capacitance?


Homework Equations


C = k * Eo * A / d



The Attempt at a Solution


I used C = 5 * 8.85*10^-12 * 4.20*10^-6 / 1*10^-8 = 1.9E-8 F

However this is not the correct answer and I am perplexed as to why. Is Eo not 8.85*10^-12 or is d not just the thickness?
 
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  • #2
So is this a parallel plate capacitor with with a dielectric in between? If so then you should be able to just use

[tex]C = \epsilon_r C_{vac}[/tex]

where [itex]\epsilon_r[/itex] is the dielectric constant. I think you may have used the wrong electric permitivity.
 
  • #3
Maybe your units are incorrect.
 
  • #4
I think the permittivity is correct, 8.85e-12 is the vacuum permittivity, and it was multipled by 5, the dielectric constant.

If you are doing this as a web-based problem, it's probably a matter of significant digits. Use more.
 

Related to How Is the Capacitance of an Axon Modeled as a Capacitor Calculated?

1. What is a capacitor?

A capacitor is an electronic component that stores and releases electrical energy. It consists of two conductive plates separated by an insulating material called a dielectric.

2. How does a capacitor work?

A capacitor works by accumulating positive and negative charges on its two plates, creating an electric field between them. When connected to a power source, the capacitor charges up and stores energy. When the power source is disconnected, the stored energy is released.

3. What is the unit of measurement for capacitance?

The unit of measurement for capacitance is Farad (F). However, for practical purposes, capacitors are usually measured in microfarads (μF) or picofarads (pF).

4. What factors affect the capacitance of a capacitor?

The capacitance of a capacitor is affected by three factors: the area of the plates, the distance between the plates, and the type of dielectric material used. Increasing the area of the plates or decreasing the distance between them will increase the capacitance, while using a material with a higher dielectric constant will also increase the capacitance.

5. Can a capacitor hold a charge indefinitely?

No, a capacitor cannot hold a charge indefinitely. Over time, the charges on the plates will dissipate due to leakage currents and the capacitor will lose its stored energy.

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