How does electricity behave in bodies of water?

Question

Everyone knows water conducts electricity (pure water doesn't, but water with solutes does, which is everything but distilled water).

If you drop a toaster (not necessarily a toaster, just an example.) in a bath tub, you'd be severely electrocuted, how ever, what would happen if did the same in the ocean?

Would there be an area in which it would be dangerous? Would it be along the surface of the water, or would it try to go straight down to the bottom? Would increasing the voltage (or amp's) increase the area of electricity or would it be the same but more severe?

This question is just out of curiosity.

Answer 1

On a pure spherical conductor, charges spread out evenly across their surface.  The earth is a spherical conductor, but it has a lot of irregularities and different resistances. On the scale of a human, and on a homogeneous medium (like water), I think that charge would appear to spread into the earth as well as just along the surface, traveling evenly in all directions.  The dispersing charge would create a voltage potential field that decreases as it radiates out from the source, similar to how a light gets dimmer as you get farther away.  So if you were in the ocean and very close to a dropping toaster, you would probably get electrocuted.  But if you were sufficiently far away, let's say 10 feet or so, you might feel just a tickle of electricity, and then eventually, like 100' or so you would feel nothing.  

I have not tested this hypothesis, but I think it's reasonable.  It is well documented that this happens when lightning strikes the ground.  From the point of impact, a decreasing voltage field radiates outward through the ground.  If you are standing near the lightning, you can get shocked just from touching the ground.  The farther your feet are apart from each other, the greater the potential difference from one foot to the other, and the greater your potential to get shocked.  for this reason they tell you to crouch but not lie down on the ground and keep your feet together if caught outside in a nasty electric storm.  I have also heard that cows get shocked easier by nearby lightning than people because their feet are farther apart.  Lightning is obviously much more powerful than a toaster, so it's deadly effect would travel much farther.  The toaster in the ocean may only be deadly within a couple feet (I'm totally guessing of course), whereas lightning can be dangerous within hundreds of feet.  Have you seen the youtube video where lightning strikes near a soccer field and lots of the players get shocked?  So increasing the voltage on your toaster would make this dispersing  electric field grow bigger--eventually you could make the voltage as high as a lightning bolt and then you'd really have a deadly toaster.  Amps and volts go hand-in-hand, so you have to increase the volts to increase the amps (within the same medium).  

BTW, the toaster is much worse in a bathtub because the charge cannot disperse evenly in all directions like it would in the ocean--it's confined to the bathtub and forced to ground through the plumbing.  I wouldn't take a bath during a lightning storm for the same reason.  Direct hit to your plumbing and you might be toast.