The field is a magnetic field around the wire, not an electric field. If you have some wire on you, that wire will get a little bit of current flowing through it if you get close.
This is actually how those shoplifting alarms work. Expensive items have a tag on them with a coil of wire connected to a radio emitter. The scanners at the exit of the store create a magnetic field and are listening for that radio wave. When you pass between the scanners, it will cause just enough current to flow in the tag to emit the radio waves and trip the alarm!
Latest Answers