Question

Cell Membranes and Dielectrics

Many cells in the body have a cell membrane whose inner and outer surfaces carry opposite charges, just like the plates of a parallel-plate capacitor. Suppose a typical cell membrane has a thickness of 6.1×10^−9 m, and its inner and outer surfaces carry charge densities of −7.7×10−4 C/m^2 and +7.7×10^−4 C/m^2, respectively. In addition, assume that the material in the cell membrane has a dielectric constant of 3.1

(a) Find the direction of the electric field within the cell membrane. a) into the cell b) out of the cell

(b) Find the magnitude of the electric field within the cell membrane.

(c) Calculate the potential difference between the inner and outer walls of he membrane (Note: express answer in millivolts,)

(d) Which wall has the higher potential a) inner wall b) outer wall   

Into the cell

Out of the cell

(b) Find the magnitude of the electric field within the cell membrane.

E=E= Answer NCNC

(c) Calculate the potential difference between the inner and outer walls of the membrane. (NOTE: Express your answer in millivolts, mV.)

ΔV=ΔV= Answer mVmV

(d) Indicate which wall of the membrane has the higher potential.

Inner wall

Outer wall

Answer 1

The given values are:

The value of charge density C/m2

Thickness or seperation between the plate m

The value of diselectric constant k = 3.1

Part (a)

The direction of electric field always from the positive charge (+) to the negative charge (-). So, in this case, the electric field is from the outer surface to the inner surface.

Part (b)

As cell membrane whose inner and outer surfaces carry opposite charges, just like the plates of a parallel-plate capacitor, So in order to calculate the magnitude of the Electric field can be calculated using the parallel-plate capacitor. i.e.

E = 0.2805 x 108 N/C

E = 28.05 x 106 N/C

Part (C)

The electric field will be constant between the plates, and zero at outside.

So,

Potential difference = Electric field x thickness

dV = 0.1711 V

Voltage at Inner side = 0.1711 V

Voltage at outside = 0V

Part (d)

Positive charge means higher potential. So, outer wall of membrane has higher potential.