The knifefish species Electrophorus electricus shown in the figure below is not

Question

The knifefish species Electrophorus electricus shown in the figure below is not really an eel, but it can grow up to 2 m long and generate a potential difference of 600 Vbetween a region just behind its head and its tail. The fish can stun or kill by sending large quantities of charge through its target. The charge comes from Hunter's organ, which in this instance is made up of 70 chains of 4,000 stacked cells called electrocytes. Each disk-shaped electrocyte has a diameter of approximately 1.8 mm and a height of about 0.4 mm, and cells are stacked as shown in the detail of the figure below. Assume the oily innards of the fish have a dielectric constant of ? = 104

(a) Model an electrocyte as a disk-shaped parallel-plate capacitor and find the capacitance of such a cell.

(b) If the electrocytes in a chain are stacked so that the capacitance combines in parallel and the chains are in turn also combined in parallel, what is the total capacitance of Hunter's organ?

(c) Use this model to find how much charge is on the head and tail of the fish when the maximum voltage is generated.

Could anyone answer this question showing work and show how to solve for A in part (a)? thanks

Explanation / Answer

A) radius = 1.8/2 mm = 0.9mm

area = pi*radius*radius

capacitance = k0A/d = 104 * 8.85 * 10-12 * pi * 0.9 * 0.9 * 10-6 / (0.4 * 10-3 ) = 5.8524*10-12 Farad Answer

B) ceq = sum of all capacitors = 70*4000*5.8524*10-12 = 1.639*10-6 Farad Answer

C) charge = ceq*Voltage = 1.639*10-6 * 600 = 0.9834*10-3 C Answer

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