can you be electrocuted by a large battery a few feet from you in seawater?
No, you are unlikely to be electrocuted by a large battery a few feet from you in seawater, despite seawater being a good conductor. Here's why:
Electricity Follows Path of Least Resistance: While seawater conducts electricity, the human body offers much higher resistance compared to the surrounding water. Electricity will naturally take the path of least resistance, meaning it's more likely to flow through the seawater directly than through your body.
Distance Matters: The farther you are from the battery, the weaker the electrical field becomes. A few feet away, the current reaching you from the battery would likely be too weak to cause harm.
Rapid Discharge: When a large battery comes into contact with seawater, it might rapidly discharge due to the short circuit created by the conductive water. This rapid discharge would further reduce the voltage reaching you.
Of course staying with the boat won't save you from the shark... the boat sank and sometime you need to go to the surface to breath, unless you happen to have like a few dozen filled scuba tanks on board and the shark decides to go away after a while AND the boat sinks in fairly shallow water ( 100 feet or so ).
BTW, the sharks attack swimmers on the surface because they think you are a seal of a large fish in trouble... they bite and decide you don't taste all that good to them. You are not their normal prey. That said a single bite can kill you with the blood loss... not to mention the blood in the water might cause other sharks to attack you by mistake. The best think is to ride that boat to the shallow bottom with the scuba tanks and hang out, sharks don't like to attack from above you. Stay on the bottom and carefully move to the shore. The big battery will not electrocute you in any case.