Question

he membrane that surrounds a certain type of living cell has a surface area of 6.0 x 10-9 m2 and a thickness of 1.6 x 10-8 m. Assume that the membrane behaves like a parallel plate capacitor and has a dielectric constant of 5.4. (a) The potential on the outer surface of the membrane is 86.2 mV greater than that on the inside surface. How much charge resides on the outer surface

Answer 1

`1.54481175* 10^(-12)\ C`

Step-by-step explanation:

`\epsilon_0` = Permittivity of free space =
`8.85* 10^(-12)\ F/m`

A = Area =
`6* 10^(-9)\ m^2`

d = Thickness =
`1.6* 10^(-8)\ m`

k = Dielectric constant = 5.4

V = Voltage = 86.2 mV

Charge is given by

`Q=CV\\\Rightarrow Q=k\epsilon(A)/(d)V\\\Rightarrow Q=5.4* 8.85* 10^(-12)* (6* 10^(-9))/(1.6* 10^(-8))* 86.2* 10^(-3)\\\Rightarrow Q=1.54481175* 10^(-12)\ C`

The charge on the outer surface is
`1.54481175* 10^(-12)\ C`