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Assume the length of an axon membrane of about 0.10 cm is excited by an action potential (length excited = nerve speed ✕ pulse duration = 50 m/s ✕ 2.0 ms = 10 cm). In the resting state, the outer surface of the axon wall is charged positively with K+ ions and the inner wall has an equal and opposite charge of negative organic ions, as shown in the figure below. Model the axon as a parallel-plate capacitor and take C = ??oA/d and Q = CΔV to investigate the charge as follows. Use typical values for a cylindrical axon of cell thickness d = 1.6 ✕ 10−8 m, axon radius r = 1.2 ✕ 101 ?m, and cell-wall dielectric constant ? = 2.3. A diagram shows a collection of positive and negative charges in and around an axon. The diagram is divided into three sections, one on top of the other. The top section is labeled "External fluid". A row of positive charges labeled "Positive charge layer" lies along the bottom side of this section. Above the row of positive charges, there is an even mixture of positive and negative charges. The middle section has thickness d and is labeled "Axon wall membrane". There are no charges in this section. The bottom section is labeled "Internal fluid". A row of negative charges labeled "Negative charge layer" lies along the top side of this section. Below the row of negative charges, there is an even mixture of positive and negative charges that is less dense than the mixture of charges in the external fluid. The axon radius r is drawn from a point in the internal fluid's mixture of charges to the center of the axon wall membrane. (a) How much energy does it take to restore the inner wall of the axon to −7.0 ✕ 10−2 V from +3.0 ✕ 10−2 V? (Assume that no energy is required to first restore the potential to 0 V from the excited potential of +3.0 ✕ 10−2 V.)  J (b) Find the average current in the axon wall during this process. (Hint: The time required to return to the resting state is 3.0 ms.)

Assume the length of an axon membrane of about 0.10 cm is excited by an action potential (length excited = nerve speed ✕ pulse duration = 50 m/s ✕ 2.0 ms = 10 cm). In the resting state, the outer surface of the axon wall is charged positively with K+ ions and the inner wall has an equal and opposite charge of negative organic ions, as shown in the figure below. Model the axon as a parallel-plate capacitor and take C = ??oA/d and Q = CΔV to investigate the charge as follows. Use typical values for a cylindrical axon of cell thickness d = 1.6 ✕ 10−8 m, axon radius r = 1.2 ✕ 101 ?m, and cell-wall dielectric constant ? = 2.3. A diagram shows a collection of positive and negative charges in and around an axon. The diagram is divided into three sections, one on top of the other. The top section is labeled "External fluid". A row of positive charges labeled "Positive charge layer" lies along the bottom side of this section. Above the row of positive charges, there is an even mixture of positive and negative charges. The middle section has thickness d and is labeled "Axon wall membrane". There are no charges in this section. The bottom section is labeled "Internal fluid". A row of negative charges labeled "Negative charge layer" lies along the top side of this section. Below the row of negative charges, there is an even mixture of positive and negative charges that is less dense than the mixture of charges in the external fluid. The axon radius r is drawn from a point in the internal fluid's mixture of charges to the center of the axon wall membrane. (a) How much energy does it take to restore the inner wall of the axon to −7.0 ✕ 10−2 V from +3.0 ✕ 10−2 V? (Assume that no energy is required to first restore the potential to 0 V from the excited potential of +3.0 ✕ 10−2 V.)  J (b) Find the average current in the axon wall during this process. (Hint: The time required to return to the resting state is 3.0 ms.)

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Assume the length of an axon membrane of about 0.10 cm is excited by an action potential (length excited = nerve speed ✕ pulse duration = 50 m/s ✕ 2.0 ms = 10 cm). In the resting state, the outer surface of the axon wall is charged positively with K+ ions and the inner wall has an equal and opposite charge of negative organic ions, as shown in the figure below. Model the axon as a parallel-plate capacitor and take C = ??oA/d and Q = CΔV to investigate the charge as follows. Use typical values for a cylindrical axon of cell thickness d = 1.6 ✕ 10−8 m, axon radius r = 1.2 ✕ 101 ?m, and cell-wall dielectric constant ? = 2.3.

A diagram shows a collection of positive and negative charges in and around an axon. The diagram is divided into three sections, one on top of the other.
The top section is labeled "External fluid". A row of positive charges labeled "Positive charge layer" lies along the bottom side of this section. Above the row of positive charges, there is an even mixture of positive and negative charges.
The middle section has thickness d and is labeled "Axon wall membrane". There are no charges in this section.
The bottom section is labeled "Internal fluid". A row of negative charges labeled "Negative charge layer" lies along the top side of this section. Below the row of negative charges, there is an even mixture of positive and negative charges that is less dense than the mixture of charges in the external fluid. The axon radius r is drawn from a point in the internal fluid's mixture of charges to the center of the axon wall membrane.
(a) How much energy does it take to restore the inner wall of the axon to −7.0 ✕ 10−2 V from +3.0 ✕ 10−2 V? (Assume that no energy is required to first restore the potential to 0 V from the excited potential of +3.0 ✕ 10−2 V.)
 J

(b) Find the average current in the axon wall during this process. (Hint: The time required to return to the resting state is 3.0 ms.)
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