Question

A neuron (pictured) is a body cell that creates and transmits electrical signals. To do this, it uses chemical processes to maintain an imbalance of electric charges on either side of its cell membrane, creating an electric field. In this problem, we will 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 ?? = 2 × 10−5 ? across. The thickness of the membrane is the same for most neurons: about 5 ?? = 5 × 10−9 ?. The electric field within a resting nerve membrane is about 1.4 × 107 ?/? (assuming the space within the membrane is empty), while the electric field outside the membrane is approximately 0. We could model a 1 ?? × 1 ?? section of the cell membrane as a pair of infinite parallel charged plates with one plate representing the inner edge of the membrane and the other representing the outer edge of the membrane.

f. Modeling the neuron cell body as a sphere with a 20 ?? diameter, what is the total magnitude of charge on each side of the cell membrane? (We can neglect the distance between the two sides of the membrane when calculating the surface area – why?)

g. Keeping the charge density the same, what would be the total amount of charge on each side of the cell membrane if the diameter of the cell were doubled to 40 ???

Answer 1