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.

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

First, let's find the capacitance of a cell wall.

We know, capacitance C = K e0 A / d

Given V = 70 * 10-3, k = 9, d = 7 * 10-9 meters, A = pi * r2 = pi * (25 * 10-6)2 = 1.96349 * 10-9 m2

=> C = 9 * 8.85 × 10-12 * 1.96349 * 10-9 / 7 * 10-9

=> C = 2.23418 *  10-11 F

Now, the energy that is stored in electric field of capacitor = 0.5 * C * V2

Energy = 0.5 * 2.23418 *  10-11 * (70 * 10-3)2

=> Energy = 5.47 * 10-14 Joules

Therefore, Energy stored in the electric field = 5.47 * 10-14 Joules

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