Still another hypothetical model for magnetic sensing could use the Faraday streaming effect. The Faraday streaming effect generates an electromotive force across an electrically conducting fluid moving at a velocity v lying in the same plane as a magnetic field, B. The Faraday motional electromotive force (EMF) is given by the vector integral:

Do not be suprised that the Faraday effect also involves the Lorentz force. The conducting fluid stream necessarily must contain positive and negative ions. As these charged ions pass through the magnetic field with velocity, v, the Lorentz force causes them to separate and create an electric field in the fluid perpendicular to v and B. (See Figure 2.4-2 for a simple description of the Faraday scenario.) The conductive fluid could be blood flowing in an artery, or seawater passing though gill slits as a fish swims. If v and B are mutually perpendicular vectors, then the EMF between the electrodes is EF = vBd v, and the electric field over d is simply (vB) V/M. The EMF or E-field from the Faraday effect can then be sensed by electroreceptors. Fortunately, unlike magnetoreceptors, electroreceptor structure has been well studied and documented (see Section 2.5). Note that the Faraday effect yields a signed output EMF:

where 0 is the angle between B and v (see Figure 2.4-2). If the flow velocity vector v and B are parallel, then EF = 0.

A possible model for the magnetic navigation aid for sharks makes use of the Faraday streaming effect. In this scenario, assume a shark is swimming toward magnetic east; i.e., it is swimming at right angles to the horizontal component of Be with a body velocity v. Assume that the shark's body has a much lower conductance than the seawater, so that it is effectively an insulator. Be(hor) points from the south magnetic pole toward the north magnetic pole. Thus, the direction of the Lorentz force, qv x Be(hor), for positive ions is up. This means that the top of the shark's head will be positive with respect to the bottom. As a result of this potential difference there will be an electric field surrounding the head whose sign depends on the swimming direction (east or west), and whose magnitude depends on the swimming velocity and the actual angle, 0, between v and Be(hor).

The magnitude and sign of the dc electric field around the head is sensed by the ampullae of Lorenzini (electroreceptors) on the shark's head. (See Section 2.5 for details about these organs). The head field will approach zero if the shark is swimming toward either magnetic north or south, or if it stops swimming. Thus, sensitive electroreceptors can contribute to the sensing of Be for navigation in sharks.

FIGURE 2.4-3 Another Faraday magnetoreceptor scenario. Here, an insulated "fish" moves at velocity v ± B in an ionic liquid (seawater). A high-conductivity channel of length L through the fish's body at right angles to v and B develops an EMF by the Faraday induction law of E = B |v| L V in the mutually perpendicular case. See text for discussion.

FIGURE 2.4-3 Another Faraday magnetoreceptor scenario. Here, an insulated "fish" moves at velocity v ± B in an ionic liquid (seawater). A high-conductivity channel of length L through the fish's body at right angles to v and B develops an EMF by the Faraday induction law of E = B |v| L V in the mutually perpendicular case. See text for discussion.

Another theoretical scenario than may be applicable to the sensing of the Earth's magnetic field is illustrated in Figure 2.4-3. Here is illustrated an insulated fish or torpedo-like object moving at a uniform velocity, v. In the ideal case, v is perpendicular to the magnetic field, B. Inside the fish, body conductivity is high. Two high-conductance apertures, shown by the small clear and dark circles, are opposite each other on the body, and form a conductor of length L inside the body. As this conductor moves relative to B as the fish swims, an EMF is induced in the conductor according to the differential vector form of Faraday's induction law:

If B, v, and dl are mutually perpendicular as shown in the figure, the EMF is maximum and is given by

Using numbers, if B = 1.7 x 10-5 T, v = 10 m/s, and L = 0.1 m, E = 17 |V. (This would be for a east- or west-swimming fish. E Y 0 for a north- or southswimming fish.) This EMF acting over 0.1 m produces an electric field of 170 |V/m across the head, which is large enough for an array of ampullary electro-receptors to sense.

Finally, consider a molluscan statocyst, normally apprising the animal where "up" is relative to its static body orientation. If some magnetite crystals are placed in a statocyst, it will signal the animal the vector sum of the magnetic force plus the gravity force acting on the particles and their acceleration. Now let the particles be embedded in freely moving supporting cells (such as a cluster of magnetic bacteria, Blakemore; 1975) so that the whole mass has neutral buoyancy. Now the statocyst will respond only to Be (and acceleration).

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