Some cell walls in the human body have a layer of negative...

Some cell walls in the human body have a layer of negative charge on the inside surface and a layer of positive charge of equal magnitude on the outside surface. Suppose that the charge density on either surface is \pm 0.50\times 10−3 C/m2 , the cell wall is 5.00 nm thick, and the cell-wall material is air.

Transcript

00:01 All right, so let's say the surface charge density on a cell wall is plus or minus, let's see, 0 .5 times 10 to the negative third coulams per square meter.

00:13 So part a asks, you know, if the cell wall has a thickness of five nanometers, what is the magnitude of the electric field in the wall between the two layers? so e is basically going to be sigma over epsilon knot.

00:28 So if we compute, this is going to be 5 .6 .5 times 10 to the 7th newtons per coulomb.

00:39 And then for part b, we want to find the potential difference between the cell.

00:44 So this is in magnitude, it's just going to be the electric field times this distance.

00:48 So if we multiply by 5 nanometers, this is about 0 .282 volts.

00:53 And then for c, we want to find at the volume of a typical human cell, which, not to be confused with voltage, but is 10 to the negative 16th cubic meters.

01:05 What is the total electric energy stored in the wall of a cell of a size, assuming it's a sphere? so the radius of this cell is going to be the cubed root of 3v over 4 pi, which is about 2 .88 micrometers.

01:23 And so the volume of the cell membrane, we'll call vm, is going to be 4 .5.

01:29 R squared times the thickness.

01:32 All right.

01:33 And so this is about 5 .2 times 10 to the negative 19 cubic meters.

01:38 And the energy stored in the cell is going to be the energy density of our electromagnetic field times the volume of this cell.

01:47 And so this is about 7 .36 times 10 to the negative 15th...