How Do You Calculate the Electrical Properties of a Cell Membrane?

[ussrasu]

The membrane of a cell is electrically equivalent to a parallel plate capacitor. A typical cell has a spherical shape with a radius 10 μm and it has a potential of −60 mV with respect to outside. The thickness of the membrane is about 0.01 μm, and it has a dielectric constant of 2.
Find:
(a) the capacitance,
(b) the magnitude of the electric field in the membrane,
(c) the stored electrical energy, and
(d) the magnitude of the separated charge.

Where to start on this question?

 

[member 553083]

a) The capacitance of a parallel plate capacitor is given by C = εA/d, where ε is the dielectric constant, A is the area of the plates, and d is the distance between the plates. For a spherical cell, the area of the plates is 4πr^2, so the capacitance is:C = (2 * 4πr^2)/(0.01 μm) = 8πr^2/0.01 μmb) The electric field in the membrane can be calculated using the equation E = V/d, where V is the potential difference across the membrane and d is the thickness of the membrane. Thus, the electric field in the membrane is:E = −60 mV/ 0.01 μm = -6000 V/mc) The stored electrical energy is given by U = ½CV^2, where C is the capacitance and V is the potential difference across the membrane. Thus, the stored electrical energy is:U = ½(8πr^2/0.01 μm)(-60 mV)^2 = 9.6 x 10^-3 Jd) The magnitude of the separated charge is Q = CV, where C is the capacitance and V is the potential difference across the membrane. Thus, the magnitude of the separated charge is:Q = (8πr^2/0.01 μm)(-60 mV) = 4.8 x 10^-5 C