Dielectrics (cell membrane)

[wildredhead]

Homework Statement

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 8.0×10−9 , and its inner and outer surfaces carry charge densities of -5.3×10−4 and +5.3×10−4 , respectively. In addition, assume that the material in the cell membrane has a dielectric constant of 5.4.

Find the magnitude of the electric field within the cell membrane.
Calculate the potential difference between the inner and outer walls of the membrane.

Homework Equations

E= 4(pie)kQ(sigma)
deltaV= E(deltaX)
V=4(pie)k(sigma)d

The Attempt at a Solution

I guess I am confussed on where to start...Can I use the first formula? I calculated both V and E using pie and obtained a wrong answer so can someone point me towards the right direction.

 

[jbsteele]

For the first: E= 4(pie)kQ(sigma)=4(3.14)(5.4)(5.3x10^-4)= 3.2x10^-1N/CFor the second: deltaV=E(deltaX)= 3.2x10^-1N/C(8x10^-9m)=2.56x10^-10V

 

[kerimek]

I understand your confusion and I am happy to assist you in solving this problem. The first formula, E= 4(pie)kQ(sigma), relates the electric field (E) within a dielectric material to the charge density (sigma) and the dielectric constant (k). However, in order to use this formula, we need to know the total charge (Q) within the cell membrane. From the given information, we only have the charge densities on the inner and outer surfaces, but not the total charge.

To find the total charge, we can use the charge density formula, sigma= Q/A, where A is the area of the surface. Since the cell membrane is like a parallel-plate capacitor, we can assume that the area of the inner and outer surfaces are the same. Therefore, we can calculate the total charge using the given charge densities and the thickness of the membrane.

Once we have the total charge, we can use the first formula to calculate the electric field within the membrane. Then, we can use the second formula, deltaV= E(deltaX), to find the potential difference between the inner and outer walls of the membrane. Remember to convert the thickness of the membrane to meters before plugging it into the formula.

I hope this helps guide you towards the right direction. If you have any further questions, feel free to ask. As a scientist, it is important to understand the fundamental concepts and equations, but it is also important to be able to apply them correctly to solve real-world problems. Keep practicing and you will become more confident in your abilities.