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Chapter 22: Problem 36

The electric field within a cell membrane is approximately \(8.0 \mathrm{MV} / \mathrm{m}\) and is essentially uniform. If the membrane is \(10 \mathrm{nm}\) thick, what's the potential difference across the membrane?

Short Answer

Expert verified
The potential difference across the cell membrane is 80mV.

Step by step solution

01

Understand the formula, symbols and what we are looking for.

The formula that relates electric field(E) and potential difference(V) is \(E = V/d\), where d is the distance over which the potential difference occurs. In this particular scenario, we are tasked to find the potential difference across a membrane(V), using the electric field(E) and the thickness of the membrane(d).
02

Substitute the given values into the formula

Rearranging the formula, we get \(V = E \cdot d\). Substituting the given values into the formula, we get \(V = (8.0 \times 10^6 \, \mathrm{V}/ \mathrm{m}) (10 \times 10^{-9} \, \mathrm{m})\)
03

Perform the calculation

Perform the multiplication to get V. \(V = (8.0 \times 10^6 \, \mathrm{V}/ \mathrm{m}) (10 \times 10^{-9} \, \mathrm{m}) = 80 \, \mathrm{mV}\)

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Most popular questions from this chapter

One proton is accelerated from rest by a uniform electric field, another proton by a nonuniform electric field. If they move through the same potential difference, how do their final speeds compare?

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