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 mVless 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.

Question: 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?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Energy Stored = 0.5 *C*V^2
where ,
C is the capacitance of Capacitor
V is the potential difference = 70 mV

C = k*A*eo/d
where,
k = 9.0
A = 3.14*((50/2) * 10^-6)^2 m^2
d = 7 * 10^-9 m

C = 9.0 * (3.14*((50/2) * 10^-6)^2 * 8.85*10^-12)/(7 * 10^-9)
C = 2.23 * 10^-11 F

Energy Stored = 0.5 *C*V^2
Energy Stored = 0.5 *2.23 * 10^-11*(70*10^-3)^2
Energy Stored = 5.5 * 10^-14 J

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