Capacitance of Axon: Calculate Farads

[rcmango]

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 x 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 4.70 x 10^-6 m^2, what is its capacitance?

in Farat

Homework Equations

The Attempt at a Solution

here is the equation:
View attachment untitled.bmp

there are other numbers being used as an example. I just don't know what to use for E0 if E = V/R, and I don't have V, so how do i solve this. thanks.

 

[rohanprabhu]

There is a simple formula for the capacitance of a parallel plate capacitor:

$$C = \frac{\epsilon_o A}{d}$$

 

[rcmango]

Ya thanks for the formula, but i still don't know what E0 is?

 

[StrongForce]

permittivity of free space! 8.85418782 × 10-12 m-3 kg-1 s4 A2

 

[rohanprabhu]

permittivity of free space! 8.85418782 × 10-12 m-3 kg-1 s4 A2

yes.. but it won't work in this case, as the medium is different than free space [di-electric constant = k = 5, here]. So the formula will be:

$$C = \frac{\epsilon_o kA}{d}$$

where k [in this example] is 5.