A long straight wire makes a magnetic field of about 0.2 µT times the current in amperes divided by the distance in metres, so 1 A at 1 cm makes 20 µT, about the strength of the Earth’s own field.
B = μ0I/2πr, and μ0/2π is 2×10⁻⁷ T m/A. So 100 A at 1 m is 20 µT again, and 10 A at 10 cm is 20 µT as well: what matters is the current over the distance. A wire carrying 20 A will swing a compass at 1 cm, and at a metre it is lost in the Earth’s field.
It is for a long, straight wire alone. A loop, a coil or a magnet follows different laws (a magnet’s field falls as the cube of the distance, much faster than a wire’s), two wires with opposite currents, like the two conductors of a mains lead, nearly cancel each other, and iron nearby changes it.
Estimate with the rule, then check it against the calculator that models it properly.
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