# Homework Help: Magnitude of electric field across cell membrane

1. Feb 25, 2016

### krbs

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
ε = V/r

3. 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.

2. Feb 25, 2016

### collinsmark

(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.)

3. Feb 25, 2016

### krbs

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

4. Feb 25, 2016

### collinsmark

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)?

5. Feb 26, 2016

### 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.

6. Feb 26, 2016

### collinsmark

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.)

7. Feb 26, 2016

### krbs

Alright, thanks so much for your help