Question

Electrofishing (a) From the definition of current density, I = ? J · d?, what is the total current between two concentric metal spheres with radii r1 and r2 (r1 < r2) separated by a material with conductivity (not surface charge density!) ? and held at constant potential difference ?V? (b) Calculate the resistance of the configuration. What does it become when one shell is much larger than the other? Why is this so? (c) Electrofishing is the practice of shocking fish (which paralyzes them and is generally unpleasant) in order to scoop them aboard a boat. One of the simplest configurations for electrofishing boats to have is a pair of small spheres lowered into the water from opposite ends of the boat (so that the approximation of part (b) holds) and held at some potential difference ?V. If you want to fish for mackerel with spherical electrodes of radius 15 cm, and you know mackerel are typically stunned by currents of 35 A, what is the voltage you would need to pulse in order to catch one? Note that sea water, in which mackerel live, has a conductivity of about 5 S/m. Hint: you can think of each of the spherical electrodes as the inner part of the concentric sphere configuration described in parts (a) and (b), with the approximation from part (b) of infinite outer radius.

          Electrofishing
(a) From the definition of current density, I = ? J · d?, what is the total current between two concentric metal spheres with radii r1 and r2 (r1 < r2) separated by a material with conductivity (not surface charge density!) ? and held at constant potential difference ?V?
(b) Calculate the resistance of the configuration. What does it become when one shell is much larger than the other? Why is this so?
(c) Electrofishing is the practice of shocking fish (which paralyzes them and is generally unpleasant) in order to scoop them aboard a boat. One of the simplest configurations for electrofishing boats to have is a pair of small spheres lowered into the water from opposite ends of the boat (so that the approximation of part (b) holds) and held at some potential difference ?V. If you want to fish for mackerel with spherical electrodes of radius 15 cm, and you know mackerel are typically stunned by currents of 35 A, what is the voltage you would need to pulse in order to catch one? Note that sea water, in which mackerel live, has a conductivity of about 5 S/m. Hint: you can think of each of the spherical electrodes as the inner part of the concentric sphere configuration described in parts (a) and (b), with the approximation from part (b) of infinite outer radius.

Electrofishing
(a) From the definition of current density, I = ? J · d?, what is the total current between two concentric metal spheres with radii r1 and r2 (r1 < r2) separated by a material with conductivity (not surface charge density!) ? and held at constant potential difference ?V?
(b) Calculate the resistance of the configuration. What does it become when one shell is much larger than the other? Why is this so?
(c) Electrofishing is the practice of shocking fish (which paralyzes them and is generally unpleasant) in order to scoop them aboard a boat. One of the simplest configurations for electrofishing boats to have is a pair of small spheres lowered into the water from opposite ends of the boat (so that the approximation of part (b) holds) and held at some potential difference ?V. If you want to fish for mackerel with spherical electrodes of radius 15 cm, and you know mackerel are typically stunned by currents of 35 A, what is the voltage you would need to pulse in order to catch one? Note that sea water, in which mackerel live, has a conductivity of about 5 S/m. Hint: you can think of each of the spherical electrodes as the inner part of the concentric sphere configuration described in parts (a) and (b), with the approximation from part (b) of infinite outer radius.

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