91Ó°ÊÓ

• Voltage across a membrane is:\(80.0{\rm{ }}mV\)
• Thickness of the membrane is: \(9.00{\rm{ }}nm\)

The potential difference between two points separated by a distance\(d\)in a homogeneous electric field of magnitude\(E\)is\(\Delta V = Ed{\rm{ }}......(1)\).

Now, calculate voltage across the membrane:

\(\begin{array}{c}\Delta V = (80.0mV)\left( {\frac{{1\;V}}{{1000\;V}}} \right)\\\Delta V = 80.0 \times {10^{ - 3}}\;V\end{array}\)

Now calculation for the thickness of the membrane:

\(\begin{array}{c}d = (9.00\;nm)\left( {\frac{{1\;m}}{{{{10}^9}\;nm}}} \right)\\d = 9.00 \times {10^{ - 9}}\;m\end{array}\)

The electric field strength in the membrane is found by solving Equation for\(E\):

\(E = \frac{{\Delta V}}{d}\)

Entering the values for\(\Delta V\)and\(d\), we obtain:

\(\begin{array}{c}E{\rm{ }} = \frac{{80.0 \times {{10}^{ - 3}}\;V}}{{9.00 \times {{10}^{ - 9}}\;m}}\\E = 8.89 \times {10^6}\;V/m\end{array}\)

Therefore, the value is obtained as \(8.89 \times {10^6}\;V/m\).