# Magnitude of the electric field across cell membranes

• krbs
In summary, 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.
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.

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.

krbs said:

## 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.

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.)

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

krbs said:
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)?

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.

krbs said:
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.)

Alright, thanks so much for your help

collinsmark
How do I deal with electric density of cell membrane

chris jats said:
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.

## What is the magnitude of the electric field across cell membranes?

The magnitude of the electric field across cell membranes varies depending on the type of cell and its function. Generally, it can range from 0.001 to 0.1 V/m.

## How is the magnitude of the electric field across cell membranes measured?

The magnitude of the electric field across cell membranes can be measured using techniques such as patch clamping, voltage-sensitive dyes, or electrophysiology.

## What is the role of the electric field in cell membrane function?

The electric field across cell membranes plays a crucial role in various cellular processes, including cell signaling, ion transport, and cell-to-cell communication.

## What factors can affect the magnitude of the electric field across cell membranes?

The magnitude of the electric field across cell membranes can be influenced by factors such as membrane potential, ion concentrations, membrane composition, and presence of ion channels and transporters.

## How does the magnitude of the electric field across cell membranes contribute to disease and disorders?

Imbalances in the electric field across cell membranes have been linked to various diseases and disorders, such as cardiac arrhythmias, neurological disorders, and muscular disorders. Understanding and regulating the electric field can be important for treating and preventing these conditions.

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