Question 1:
A neuron is a body cell that functions to create and transmit electrical signals. To do this, it uses chemical processes to maintain an electrical potential difference across its cell membrane. In this problem we will use our knowledge of electrical relationships to estimate the amount of charge on the membrane. Neurons come in a range of sizes, but a typical one may have a cell body of 20 um (2 x 10-5 m) across.
The thickness of the membrane is the same for most neurons about 5 nm (5 x 10-9 m). The potential difference across a resting nerve membrane is about 70 mV (70 x 10-3 V). Well model a piece of the cell membrane 10 μm x 10 μm across as a pair of infinite parallel plates separated by a distance d = 5 nm, with one plate representing the inner edge of the membrane and the other representing the outer edge of the membrane.
A. Assuming the space separating the two plates of our membrane is empty space, calculate the electric field between the plates.
B. Using the electric field you found in part A, calculate the charge density, σ (charge per unit area), on the plates. (Hint: The E field near to a single plate of charge having a uniform charge density σ, is 2Πkcσ where kc = 9 x 109 N-m2/c2.)
C. Using the charge density you found in B, calculate the magnitude of the charge on each side of the piece of cell membrane we are modeling and the net charge on the piece of the membrane.
D. Do you think our model of the electric fields and potentials in a cell membrane as infinite parallel plates is a good one? Give reasons for your judgment.
Question 2:
1. In chemistry, one often uses a unit of charge known as the Faraday, F, which has the magnitude of the charge of 1 mole of electrons. Since the Coulomb has come to be the international standard of unit of charge, the Faraday is taken to have the unit "C/mole" or Coulombs/mole. How many Coulombs/mole is there in a Faraday?
F is a very large charge. Consider two small aluminum spheres of 1 gram each hanging by 23 cm long non-conducting threads. The two spheres repel and settle down to hang as shown in the figure at the right. Suppose that the two spheres share the charge equally.
1 Estimate the charge on each sphere.
2 How many moles of excess electrons is that?
3 How many Faradays of charge does that correspond to?
Question 3:
In the figure at the right are shown four configurations of charge labelled A, B, C, and D. The small circles are meant to represent point (i.e., very small) charges and the long rectangles are meant to represent infinite (i.e., large flat) sheets of charge whose area is perpendicular to this page. Through each figure is drawn a dotted line representing the x-axis of a coordinate system with the origin indicated by 0. (The y-axis is not shown.)
Below are shown some graphs, some of which might represent a graph of either the electrostatic potential or the x-component of the electric field at the locations along that axis in the various cases. Fill in the table below by identifying which graphs would work for each case. If more than one would work, give all that are correct. If none work, put N.
