Electrical conductivity comparisons in laymans terms/ Electro receptor range.

[The Jack]

So if I look at how conductive things are I get numbers like 1311999.75753^1010101

Look, I don't even know how to write the example.

So, here's my hypothetical.

In seawater, If a shark's electroreceptors lets her detect a fish's biolelectricity within a metre (An approximated example from a website that I hope is right) how far away could they detect that same fish in the common form of the following:
sand
dirt
wood
concrete
common rock
Steel
Aluminium
In heavy fog or rain if that's not crazy?

Also, at what range could said shark detect your average mobile phone or camera in these mediums (Yes, ignore that they can't work in these mediums unless there's a way to get them to work in these mediums)

[Tirunedeth]

Firstly, reading about how sharks detect electric fields, I'm not sure if they can do something other than seawater. It sounds to me like the ampullae of Lorenzini are adapted to the electrical properties of seawater, and I'm not sure if they'll work as well - or at all - in, say, air. However, I'm going to ignore this concern, and just look at how different materials affect the strength of the electric field, since that's what I can confidently answer. And also since I'm not sure if you're talking about literal sharks swimming through solid steel, or just using a shark's ability to sense electric fields as a reference for some other fictitious creature.

It turns out that conductivity is the wrong measure for what you want to know. What we actually want is permittivity. The former is a measure of how the presence of an electrical field produces a current while the latter is a measure of how an electrical field produces a state of separated charge. While there is correlation, there are some exceptions - e.g., adding salt to water increases its conductivity, but at least according to a quick look around the Internet reduces its permittivity (although, now that I think about it, that may have been for higher frequency electric fields - there can be big differences between the behavior of materials in response to a low frequency or a static electric field and those at higher frequencies).

To make things as simple as possible, the strength of the electric field at a particular distance from a charge distribution is multiplied by a factor of one over the ratio of the new permittivity to the old permittivity. This means that the range for a detector with a certain sensitivity will increase by a factor of the square root of the ratio of the reference permittivity to the new permittivity (assuming point source like behavior).

For example, water looks to have a relative permittivity of between 60-80. Looking at your list of materials, concrete and rock both seem to have relative permittivities of around 5-15 (sand and dirt are probably similar when dry, but the presence of water will throw things off). This gives a range of sqrt(60/15) to sqrt(80/5), or 2-4 times that in water. (Dry) wood is around 2 or so, which (dispensing with ranges here) gives a range factor of around sqrt(70/2) ~= 6. Steel and aluminum effectively have extremely high permittivities (often modeled as infinite, apparently), so the hypothetical steel-shark would have essentially no ability to detect electric fields in these materials. I don't think that even heavy fog is going to increase the permittivity of air much beyond one, so I'd guess the range in any type of air would be around sqrt(70) ~= 8.

If you want to look up other materials, there are a couple other terms you can use. I've been describing things in terms of relative permittivity, which is also called dielectric constant. You can also use absolute permittivity so long as you're using it for both numbers, or you can convert from absolute to relative by dividing by the permittivity of free space. Finally, the electric susceptability can be converted to a relative permittivity simply by adding one.

[The Jack]

Could you perchance simplify further

[Ninja_Prawn]

This gives a range of sqrt(60/15) to sqrt(80/5), or 2-4 times that in water. (Dry) wood is around 2 or so, which (dispensing with ranges here) gives a range factor of around sqrt(70/2) ~= 6. Steel and aluminum effectively have extremely high permittivities (often modeled as infinite, apparently), so the hypothetical steel-shark would have essentially no ability to detect electric fields in these materials. I don't think that even heavy fog is going to increase the permittivity of air much beyond one, so I'd guess the range in any type of air would be around sqrt(70) ~= 8.

I know nothing about sharks or bioelectomagnetism, and I haven't studied this kind of physics since about 2009, but instinctively this feels backwards. Surely the more permittive materials will provide a longer detection range? The wiki page on electroreception even says that it's only found in aquatic animals because it's more effective in water than in air. I feel like the ratio needs to be new:old.

As for asking a shark to detect electrical devices in water, I'd assume they can do so easily over very long distances. Apparently the radiation from undersea telegraph cables was strong enough that sharks suffered injuries from it, before they started using optical fibre.

[Gray Mage]

I know nothing about sharks or bioelectomagnetism, and I haven't studied this kind of physics since about 2009, but instinctively this feels backwards. Surely the more permittive materials will provide a longer detection range? The wiki page on electroreception even says that it's only found in aquatic animals because it's more effective in water than in air. I feel like the ratio needs to be new:old.

As for asking a shark to detect electrical devices in water, I'd assume they can do so easily over very long distances. Apparently the radiation from undersea telegraph cables was strong enough that sharks suffered injuries from it, before they started using optical fibre.

The more permittive the material is, the smaller the electrical field is (if you were to compare how strong the electrical field is x meters from the same charge source, the more permittive material would have the weaker field). Since the electrical field is inversely proportional to the permittivity of the material and to the square of the distance, it means that if you were to have a material 4 times less permittive as another, you'd need to be twice as far from the same charge source on the lesser permittive material to be subjected to the same electric field. On the extreme, good eletrical conductors (like most metals) have an almost infinite permittivity, so they have null electric fields inside them (because the charge has free mobility and disperses in a configuration that has the lowest possible potential and is uniformly distributed). So a more permittive material would have a shorter range.

I'd assume/infer that it being more effective in water has to do with how it detects (the physical/chemical composition of the sensor and its interaction with electric fields) the field, not with how strong the field would be.