Question

The membrane that surrounds a certain type of living cell has a surface area of 4.4 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 4.1. (a) The potential on the outer surface of the membrane is +66.4 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?

Answer 1

C=q/ Δφ,
C=εε₀A/d,
q/ Δφ = εε₀A/d,
q= εε₀A Δφ /d,
where ε =4.1, ε₀=8.85 •10⁻¹² F/m,
A=4.4•10⁻⁹m²,
d=1.64.4•10⁻⁸ m,

N=q/e=q/1.6•10⁻¹⁹ = …