2.3. Sharks and other elasmobranch sh use their AoL electrosensors to locate wounded prey sh lying on the ocean oor . This problem will model a wounded sh and calculate the electric eld in the w ater at some distance R and angle . from the sh. The wounded sh is represented by an electric dipole. Assume that the sh has major w ounds on its head and tail, and thus may be represented electrically as two conductors separated by a thin insulator (its body) of length L. The wounds have a potential difference between them of VF V, and an electrical capacitance between them of CF F. Thus, at a distance R > L, the wounded sh can be represented by an electrical charge dipole. See Figure P2.3. The equivalent charges on the ends of the sh are Q = C FVF C, and its dipole moment is p = QL = CFVF L C meters. Consider the sea bottom to have the same dielectric constant as water (80), and not to introduce a boundary condition on the electric eld. Ne glect conductivity effects. A well-considered problem in electrostatics is the computation of the electric eld produced by a char ge dipole at a point (L, .). In cylindrical coordinates, the electric eld has two components given by*:
where ar and a. are unit vectors, and . is the angle the radial line makes with the dipole axis.
a. Calculate |e| at the shark, given: L = 0.2 m, CF = 80 pF, VF = 50 mV, R = 2 m, . = 30°, eo = 8.85 • 10-12 F/m, and . (dielectric constant of water) 80.
b. *Using the numbers above, nd the R where |e| = 0.2 ^V/m.
2.4. The stalk and mass of a tricholith of an Arenivaga cockroach are restrained from moving by a stiff torsion spring when the animal is tilted. Tilting the cercus, as shown in Figure P2.4, generates a torque, M., which is sensed by a strain-sensitive, mechanoreceptor cell. The output spike frequency of the cell is given by: fo = KM.. (There is no spike output for any tilt in the other direction.) Give an expression for the ring frequenc y as a function of . .
* Kraus, J.D. 1953. Electromagnetics, McGraw-Hill, New York, Ch. 2. © 2001 by CRC Press LLC
Was this article helpful?
This guide will help millions of people understand this condition so that they can take control of their lives and make informed decisions. The ebook covers information on a vast number of different types of neuropathy. In addition, it will be a useful resource for their families, caregivers, and health care providers.