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BIO Cell Membranes and Dielectrics Many cells in the body
Chapter 20, Problem 97GP(choose chapter or problem)
Problem 97GP
BIO Cell Membranes and Dielectrics Many cells in the body have a cell membrane whose inner and outer surfaces carry opposite charges, just like the plates of a parallel-plate capacitor. Suppose a typical cell membrane has a thickness of 8.1 × 10-9 m, and its inner and outer surfaces carry charge densities of −0.58 × 10 3 C/m2 and +0.58 × 10-3 C/m2, respectively. In addition, assume that the material in the cell membrane has a dielectric constant of 5.5. (a) Find the direction and magnitude of the electric field within the cell membrane, (b) Calculate the potential difference between the inner and outer walls of the membrane, and indicate which wall of the membrane has the higher potential.
Questions & Answers
QUESTION:
Problem 97GP
BIO Cell Membranes and Dielectrics Many cells in the body have a cell membrane whose inner and outer surfaces carry opposite charges, just like the plates of a parallel-plate capacitor. Suppose a typical cell membrane has a thickness of 8.1 × 10-9 m, and its inner and outer surfaces carry charge densities of −0.58 × 10 3 C/m2 and +0.58 × 10-3 C/m2, respectively. In addition, assume that the material in the cell membrane has a dielectric constant of 5.5. (a) Find the direction and magnitude of the electric field within the cell membrane, (b) Calculate the potential difference between the inner and outer walls of the membrane, and indicate which wall of the membrane has the higher potential.
ANSWER:
Solution 97 GP:
Step 1 of 2:-
a)
Here, we have to calculate the magnitude and direction of the electric field inside the cell membrane.
The outer charge density we can call
The inner charge density can be called as .
The net electric field inside is,
.
The magnitude of the electric field is and the direction is from the positive surface charge density to the negative charge density.