We can physically model the axonal membrane (axolemma) as a parallel plate capacitor with dielectric in it. If the capacitance per unit area in F/m^2 is known, what single additional parameter needs to be measured in order to determine the dielectric constant k of the membrane material?
a) No other measurement is necessary
b)
The area of the capacitor
c) The permittivity of free space E0
d) The thickness of the membrane
e) The resistance of the membrane
I know the answer is C but i don't know how to prove it mathematically or logically. Any help?
kappa = Cd/Eo A
C/A is given
Eo can be looked up
so....
So the correct answer would be c) right?
To determine the dielectric constant (k) of the membrane material, one additional parameter needs to be measured. Let's analyze each option to understand why the answer is option C.
a) No other measurement is necessary: This option implies that the dielectric constant can be directly determined from the capacitance per unit area alone. However, this is not correct because capacitance depends on the permittivity (ε) of the material as well, which is related to the dielectric constant as ε = k * ε₀. So, the dielectric constant cannot be determined solely from the capacitance per unit area.
b) The area of the capacitor: The area of the capacitor only determines the overall capacitance, but it does not give any information about the dielectric constant of the membrane material.
c) The permittivity of free space (ε₀): This is the correct answer. The permittivity of free space (ε₀) is a fundamental constant in physics that is already known (~8.85 x 10⁻¹² F/m). The dielectric constant (k) is related to the capacitance (C) of the parallel plate capacitor by the equation C = (k * ε₀ * A) / d, where A is the area of the capacitor and d is the thickness of the membrane. By measuring the capacitance per unit area and knowing the permittivity of free space, we can rearrange the equation to solve for k.
d) The thickness of the membrane: The thickness of the membrane affects the capacitance of the parallel plate capacitor, but it doesn't help in determining the dielectric constant of the material.
e) The resistance of the membrane: The resistance of the membrane is not relevant for determining the dielectric constant. It relates to the conductive properties of the membrane rather than the dielectric properties.
Therefore, the correct answer is option C, as the permittivity of free space (ε₀) is the additional parameter that needs to be measured in order to determine the dielectric constant (k) of the membrane material.