Phys 1202 Homework #7 due Thursday, March 5, 2015 SK Chapter

Phys 1202 Homework #7
due Thursday, March 5, 2015
SK Chapter 18, Problems 3, 4, 25, 26, 30, 31.
Plus, the following three problems.
P1. The membrane of the axon of a nerve cell can be modeled as a thin cylindrical shell of
radius 1.00 × 10–5 m, having a length of 10.0 cm and a thickness of 10.0 nm. The membrane has
a positive charge on one side and a negative charge on the other, and the membrane acts as a
parallel-plate capacitor of area 2πrL and separation d. Assume the membrane is filled with a
material whose dielectric constant is 3.00. (a) Find the capacitance of the membrane. If the
potential difference across the membrane is 70.0 mV, find (b) the charge on the positively
charged side of the membrane.
P2. What is the magnitude of the electric field across an axon membrane 1.0 x 10-8 m thick if the
resting potential is -70 mV?
P3. A neuron is stimulated with an electric pulse. The action potential is detected at a point 3.40
cm down the axon 0.0052 s later. When the action potential is detected 7.20 cm from the point of
stimulation, the time required is 0.0063 s. What is the speed of the electric pulse along the axon?
(Why are two measurements needed instead of only one?)
P4. Estimate how much energy is required to transmit one action potential along an axon if the
capacitance is estimated at 1.0 ×10−8 F , and the potential difference is about 0.1 V.
[Hint: the energy to transmit one pulse is equivalent to the energy stored by charging the axon
capacitance]. What minimum average power is required for 10,000 neurons each transmitting
100 pulses per second?
P5. During an action potential, + Na ions move into the cell at a rate of about 3×10-7 mol/m2 .s.
How much power must be produced by the “active Na + pumping” system to produce this flow
against a +30 mV potential difference? Assume the axon is 10 cm long and 20µm in diameter.