Chapter 18, Problem 44P

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# Consider the model of the axon as a capacitor from Problem 43 and Figure P18.43. (a) How much energy does it take to restore the inner wall of the axon to −7.0 × 10−2 V, starting from +3.0 × 10−2 V? (b) Find the average current in the axon wall during this process.

(a)

To determine
The energy restore in the inner wall of the axon.

Explanation

Given Info: The thickness of axon wall membrane is d=1.0Ã—10âˆ’8â€‰m , dielectric constant of cell wall is k=3.0 and axon radius is r=1.0Ã—101â€‰Î¼m , The capacitance of the parallel plate capacitor is 1.67Ã—10âˆ’8â€‰F and starting potential is 7.0Ã—10âˆ’2â€‰V .

Explanation:

Formula to calculate the area of the surface of axon membrane is,

A=2Ï€rL

• A is the area of the axon membrane surface,
• R is the axon radius,
• L is the length of the axon membrane,

Substitute 1.0Ã—101â€‰Î¼m for r and 0.10â€‰m for L .

A=2(3.14)(1.0Ã—101â€‰Î¼m)(10âˆ’6â€‰m1â€‰Î¼m)(0.10â€‰m)=0.628Ã—10âˆ’5â€‰m2

Formula to calculate the capacitance of the parallel plate capacitor for model axon,

• C is the capacitance of the parallel plate capacitor,
• k is the dielectric constant,
• Îµ0 is the permittivity of free space,
• A is the area of the axon membrane surface,
• d is the thickness of axon wall membrane,

Substitute 0.628Ã—10âˆ’5â€‰m2 for A, 8.85Ã—10âˆ’12â€‰C2/Nâ‹…m2 for Îµ0 , 3.0 for k and 1.0Ã—10âˆ’8â€‰m for d to find C

(b)

To determine
The average current in the axon wall.

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