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Membrane walls of living cells have surprisingly large electric fields across them due to separation of ions. (Membranes are discussed in some detail in Nerve Conduction—Electrocardiograms.) What is the voltage across an 8.00 nm–thick membrane if the electric field strength across it is 5.50 MV/m? You may assume a uniform electric field.
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Final Answer

$44.0 \textrm{ mV}$

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OpenStax College Physics for AP® Courses Solution, Chapter 19, Problem 19 (Problems & Exercises) (0:56)

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Video Transcript

This is College Physics Answers with Shaun Dychko. We are going to model the cell membrane as two large parallel plates separated by some distance <i>d</i>. Now the electric field in this case then is the potential difference between the two sides divided by the separation between them. Now, we can solve for the voltage by multiplying both sides by <i>d</i> and it’s going to be the electric field strength times separation between the layers of the membrane so its 5.50 times ten to the six volts per meter, I put ten to the six in the place of pre-fix mega in Mega-Volts and then we multiply that by the separation between the layers of the membrane which is eight nanometres and nanometres, the Nano means times ten to the power minus nine. So, eight times ten to the power minus nine meters and this works out to 44.0 milli-volts.