Question

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 8.5×10−9 m , and its inner and outer surfaces carry charge densities of -6.3×10−4 C/m2 and +6.3×10−4 C/m2 , respectively. In addition, assume that the material in the cell membrane has a dielectric constant of 5.5.

1. Find the direction of the electric field within the cell membrane.

a. into the cell

b. out of the cell

2. Find the magnitude of the electric field within the cell membrane.

Express your answer using two significant figures.

3. Calculate the potential difference between the inner and outer walls of the membrane.

Express your answer using two significant figures.

4. Indicate which wall of the membrane has the higher potential.

a. inner wall

b. outer wall

Answer 1

1)

Ans :- Into the cell.

The electric field points towards -ve charges. The inner surface of the membrane is -ve charged so the electric field lines are directed into the cell.

2)

Given :-

d = 8.5 x 10^-9 m

= 6.3 x 10^-4 C/m^2

k = 5.5

o = 8.85 x 10^-12 C^2 / N.m^2

E = / o*k

E = (6.3 x 10^-4) / (8.85 x 10^-12 x 5.5)

E = 1.3 x 10^7 N/C

c)

V = E*d

V = 1.3 x 10^7 N/C x 8.5 x 10^-9 m

V = 0.1105 V

V = 110.5 mV

d)

Ans :- Outer wall

The charge density on the outer wall on the membrane is +ve so the electric potential on the outer wall is higher.