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It's just a wire wrapped in a circle. It doesn't become a solenoid (make that linear magnetic field) until current flows through it, by applying a voltage *across* it--higher potential on one side, lower on the other, in a closed circuit. Voltage is not a level; you can't apply 12 volts *to* something. It's a relative difference, so without a circuit it's meaningless. You'd be just as accurate saying it's 0, or saying that your horn and everything else grounded to the chassis is seeing a "constant -12V". Laying your arm across a battery means having your arm complete a connection between high and low potential. Just touching one terminal would have no closed circuit, current, or shock.
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