Download The membrane that surrounds a certain type of living

The membrane that surrounds a certain type of living cell has a surface area of 5.0 10-9
m2 and a thickness of 1 10-8 m. Assume that the membrane behaves like a parallel plate
capacitor and has a dielectric constant of 5.
(a) If the potential on the outer surface of the membrane is +70.0 mV greater than that
on the inside surface, how much charge resides on the outer surface?
(b) If the charge in part (a) is due to K+ ions (charge +e), how many such ions are
present on the outer surface?
I have a problem for an assignment that I have used most of my responses for and still
can't manage to get. I tried using an equation I have for a capacitor, which didn't work,
but I managed to get the right answer for B, but can't manage to get a to work even
though they are closely connected. Please, help!!!
For the parallel plate capacitor, we have
Surface area A = 5.0 * 10-9 m2
Distance d = 1 * 10-8 m
The dielectric constant  r  5     r 0  5 0 , where  0  8.854  1012 F/m is the
permittivity of the space,
The potential difference of the two surfaces: V  70.0 mV = 0.07 V
We know the electric field between two parallel plates is
 Q/ A
E 


Then the electric field and the potential difference have the relationship of
Q/ A
Qd
V  Ed 
d

A
So the charge on the surface of the plates is
V A
Q
d
You can also use the capacitance of the parallel plates:
A
C
d
Q
Also, C 
V
Then
A Q

d
V
VA
Q
d
Now substitute the values to calculate the charges:
12
* 5.0  109
V  A 0.07 * 8.854  10
Q

 3.0989  1013 C
8
d
1  10

 

The outer surface has higher potential, so it has positive charges of 3.0989  1013 C .
(2) +e = 1.6 * 10-19 C, then we need to have
Q 3.0989  1013 C

 1936812.5 K+ ions
e
1.6  1019 C