Q .81 - Excercises And ProblemsExpert-verified
Consider a uniformly charged sphere of radius R and total cAlC charge Q. The electric field outside the sphere is simply that of a point charge Q. In Chapter 24, we used Gauss's law to find that the electric field inside the sphere is radially outward with field strength
a. The electric potential outside the sphere is that of a point charge Q. Find an expression for the electric potentialat position r inside the sphere. As a reference, let at the surface of the sphere.
b. What is the ratio
c. Graph V versus r for 0 r 3 R.
The electric potential at a position inside the sphere,
The electric field, and electric potential, outside the sphere is that of a point charge Q. The electric field inside the sphere is given by,
at the surface of the sphere
If represents electric field and V represents potential associated with it then they are related by
We have to find the potential at a point inside the sphere.
- Since the potential inside the sphere is given by,
From the expression for potential inside the sphere,
A nerve cell in its resting state has a membrane potential of , meaning that the potential inside the cell is less than the potential outside due to a layer of negative charge on the inner surface of the cell wall and a layer of positive charge on the outer surface. This effectively makes the cell wall a charged capacitor. When the nerve cell fires, sodium ions,, flood through the cell wall to briefly switch the membrane potential to . Model the central body of a nerve cell-the soma-as a diameter sphere with a -thick cell wall whose dielectric constant is 9.0. Because a cell's diameter is much larger than the wall thickness, it is reasonable to ignore the curvature of the cell and think of it as a parallel-plate capacitor. How many sodium ions enter the cell as it fires?
94% of StudySmarter users get better grades.Sign up for free