Figure P21

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


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