How Does Membrane Thickness Affect the Electric Field in a Nerve Cell?

[la3]

The cell membrane in a nerve cell has a thickness of 0.12 micrometers.
(a) Approximating the cell membrane as a parallel plate capacitor with a surface charge density of 5.9 x 10^(-6) C/m2, find the electric field within the membrane.

(b) If the thickness of the membrane were doubled, would your answer to (a) increase, decrease, or stay the same. Explain.


Can anyone help me get started on this? I think one of the formulas to use would be something like:
E = sigma / permittivity of free space
where E= electric field, sigma= charge density, and permittivity of free space= 8.85 x 10^-12

I am unsure how the membrane thickness comes into play.

 

[Doc Al]

Sounds like you're on the right track. It's up to you to determine if membrane thickness affects the field within.

 

[la3]

I cannot see how membrane thickness matters since it would only affect A (area), but A cancels from both sides of the equation.
However, since it is included in both parts (a) and (b) I feel that thickness probably matters...

 

[Doc Al]

I cannot see how membrane thickness matters since it would only affect A (area), but A cancels from both sides of the equation.

If you mean plate area, then thickness--the distance between the plates--has nothing to do with it.

However, since it is included in both parts (a) and (b) I feel that thickness probably matters...

They want to know if you know what matters and what doesn't.

 

[la3]

Well I am going to have to say that membrane thickness does not matter since the electric field is constant within a parallel plate capacitor since both plates run exactly parallel to each other.
The voltage (perpendicular to the electric field lines) will change as you move from one plate to another (ie. as equipotential lines), but the electric field remains constant.

So, for (a):
E = sigma / permittivity of free space
E = (5.9 x 10^(-6) C/m2) / (8.85 x 10^(-12) C2/Nm2)
E = 6.7 x 10^5 N/C

And for (b):
The answer to (a) would stay the same for above reasons.

How does this sound?

 

[Doc Al]

Perfecto!

 

[la3]

Haha... great! Thanks for your help!
I had a hard time visualizing the problem on my own.