Finding the electric field around an electric eel

I'm having problems solving for the electric field and the current that an electric eel generates. Would I use Gauss's law and treat it as a long charged wire? How would I find the charge of the electric eel? I'm really confused about what I can do and where to start.

In the second part of the project I need to find the current and electric field that affects the prey of an electric field also. Would this calculation be like adding a (human) resistor in a circuit?

• I don't think it makes sense to treat it as a long wire since the thickness of an eel is certainly not negligible as compared to its length. This rules out a simple symmetry-based application of Gauss' law. – Danu Jun 17 '14 at 21:07
• The body of the eel can be viewed as a large battery, the EMF inside produces potential difference between the ends. The electric field is similar to that of a pair of charges, that is a finite size dipole. Once the electric field is known (you need to assume some dimensions and voltage for that) the current through the water can be found from the Ohm law, $j=\sigma E$. – Maxim Umansky Jun 18 '14 at 1:25

Let's first make a 'textbook' calculation to get a feeling of the magnitude of the field. See below and sources for a more accurate description.

Suppose that the you can treat the eel as infinitely small. And take is length to be about 1 m long and can generate a voltage difference of 500 volts between its head and tail. Neglecting the directionality of the field, the magnitude of the field is $$|\vec{E}| = \Delta V \cdot d = 500 V/m.$$

I based this value on the following

The higher intensity charges vary by the size of the eel. Smaller eels (about 10 cm in length) can produce charges of up to 100 V. Larger eels (over 1 m in length) can produce charges of 450 to 650 volts of electricity.Source

In fact an eel generates a electric dipole, i.e. it generates a positive pole at on location and a negative pole at a different location.

As you can see from this picture the electric field runs in curves lines between this poles.

A dipole field is characterized by a inverse cubic force $$F \propto \dfrac{1}{r^3}.$$ This has a consequence that the electric field produced by the eel can only serve for communication over ranges of a few meters, for example it can only sens a prey using its field at about 1 m.

An old, quite funny question: Could we run an electric car on electric eels?

Source:

Physics in Biology and Medicine By Paul Davidovits