A typical cell has a membrane potential of -70 mV, meaning that the potential in

Question

A typical cell has a membrane potential of -70 mV, meaning that the potential inside the cell is 70 mV less than the potential outside due to a layer of negative charge on the inner surface of the cell wall and a layer of positive charge on the outer surface. This effectively makes the cell wall a charged capacitor. Because a cell's diameter is much larger than the wall thickness, it is reasonable to ignore the curvature of the cell and think of it as a parallel-plate capacitor.

How much energy is stored in the electric field of a 50-m-diameter cell with a 7.0-nm-thick cell wall whose dielectric constant is 9.0?

Explanation / Answer

here,

diameter of cell , d = 50 um

radius , r = 50 * 10^-6 m

distance between the plates , d = 7 nm

d = 7 * 10^-9 m

k = 9

capacitance , C = area *epsilon0*k/d

C = pi*(50*10^-6)^2 *8.85*10^-12*9 /(7 * 10^-9)

C = 1.79*10^-6 F

V = 70 mV

V = 0.07 V

energy stored , E = 0.5 * C*V^2

E = 0.5 * 1.79*10^-6* 0.07^2

E = 4.39*10^-9 J

the energy stored in the capacitor is 4.39*10^-9 J

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