Magnitude of the electric field across cell membranes

[krbs]

Homework Statement

The electric potential difference across a neuron cell membrane is 0.070 V. The thickness of the membrane is 5.0 x 10^-9 m.

a) Find the magnitude of the electric field across the membrane. Describe any assumptions you are making.

Homework Equations

ε = V/r

The Attempt at a Solution

ε = 0.070V/5.0 x 10^-9m
= 1.4 x 10⁷ N/C

Assuming the width of the cell membrane is constant and that the electric field across it is uniform, the magnitude of the electric field is 1.4 x 10⁷ N/C.

 

[collinsmark]

Homework Statement

The electric potential difference across a neuron cell membrane is 0.070 V. The thickness of the membrane is 5.0 x 10^-9 m.

View attachment 96439

a) Find the magnitude of the electric field across the membrane. Describe any assumptions you are making.

Homework Equations

ε = V/r

The Attempt at a Solution

ε = 0.070V/5.0 x 10^-9m
= 1.4 x 10⁷ N/C

Assuming the width of the cell membrane is constant and that the electric field across it is uniform, the magnitude of the electric field is 1.4 x 10⁷ N/C.

'Looks about right to me.

(If you were working more formally with vectors that involve direction, there might be a negative sign involved. But since you were only asked to find the magnitude, your answer looks good.)

 

[krbs]

Thanks, it's mostly the "assumptions" part I'm uncertain about

 

[collinsmark]

Thanks, it's mostly the "assumptions" part I'm uncertain about

I think you've got the big ones. The part about the electric field being uniform is perhaps the most important one.

In which situations does |E| = |V/r| hold true? Again, I think you've got most (perhaps all) of them. I'm just saying it wouldn't hold true, for example, if the membrane was sphere shaped with a small inner radius and a large outer radius (where the membrane thickness on the order of the radius of the entire cell). But I think you have that covered (at least indirectly) in your "E is uniform" assumption. Maybe you could think of an additional assumption about the approximate shape of the membrane boundaries relative to the narrow thickness of the membrane (just for an additional clarification)?

 

[krbs]

I'm not sure when E = V/r holds true, beyond it being used for two parallel plates (so only in a uniform field). I suppose the membrane boundaries need to be thin and rectangular like the membrane itself because otherwise the field would probably not be uniform.

We've not yet covered fields in a sphere; it's all been simple 2D rectangles and triangles.

 

[collinsmark]

I'm not sure when E = V/r holds true, beyond it being used for two parallel plates (so only in a uniform field). I suppose the membrane boundaries need to be thin and rectangular like the membrane itself because otherwise the field would probably not be uniform.

Approximating the membrane boundaries as parallel plates is good! Yes, that kinda goes with the assumption about the uniform electric field, but the parallel plate approximation couldn't hurt to bring up in your list of assumptions! (If for no other reason, to nail in the uniform electric field idea.)

 

[krbs]

Alright, thanks so much for your help

 

[chris jats]

How do I deal with electric density of cell membrane

 

[collinsmark]

How do I deal with electric density of cell membrane

Hello @chris jats,

Welcome to PF!

Go ahead and start a new thread. Typically we have one problem per thread on the homework sections of PF. This thread is quite old, and starting a new thread for your question would be appropriate.