Cell Membrane and Hollow Spheres

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SUMMARY

The discussion focuses on two physics problems involving electric fields and capacitance in cell membranes and hollow metal spheres. The first problem calculates the electric field across a cell membrane with a potential difference of 0.0680 V and a thickness of 7.95×10-9 m, using the formula E = |ΔV/d|. The second problem involves two concentric hollow metal spheres, where the inner sphere has a radius of 0.1440 m and a potential of 86.0 V, while the outer sphere has a radius of 0.146 m and a potential of 82.0 V. The solution requires determining capacitance using the dielectric constant of Teflon and calculating the energy stored in the space between the spheres.

PREREQUISITES
  • Understanding of electric fields and potential difference
  • Knowledge of capacitance and energy storage in capacitors
  • Familiarity with dielectric materials, specifically Teflon
  • Proficiency in using formulas for electric field (E = |ΔV/d|) and capacitance (C = (kε0A)/d)
NEXT STEPS
  • Research the properties of Teflon as a dielectric material
  • Study the derivation of electric field equations in different geometries
  • Explore advanced capacitance calculations involving multiple dielectric layers
  • Learn about the applications of electric fields in biological membranes
USEFUL FOR

Students and professionals in physics, electrical engineering, and materials science, particularly those interested in electromagnetism and its applications in biological systems and capacitor design.

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there are 2 probs here.
1) The inner and outer surfaces of a cell membrane carry a negative and positive charge, respectively. Because of these charges, a potential difference of about 0.0680 V exists across the membrane. The thickness of the membrane is 7.95×10-9 m. What is the magnitude of the electric field in the membrane?

I thought i could just use E=-change in V/change in distance, but no.

2) Two hollow metal spheres are concentric with each other. The inner sphere has a radius of 0.1440 m and a potential of 86.0 V. The radius of the outer sphere is 0.146 m and its potential is 82.0 V. If the region between the spheres is filled with Teflon, find the electric energy contained in this space.

This one i played with in the equation V=(kq/rsquared)+(k/q'/rsquared).
I've just confused myself with working them so many times. so I am seeking help here!
 
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(1) asks for magnitude, so I think it's just [itex]E = \left | \frac{\Delta V}{d} \right |[/itex]

(2) determine the capacitance using the potential difference, the distance between the spheres, and the dielectric constant of the teflon. Then you can find the amount of energy stored using the potential difference and the capacitance.
 
i figured it out.
(1) I set V=kq/r equal to E=kq/r^2

(2) i solved Q=[(kEoA)/d]V
and then plugged into V=EPE/Q

its easier for me if the equations are
derived, and i worked it all out nicely.
That second problem was making me crazy!
 

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