Question

When an electric circuit is passed through any wire ,a magnetic field is produced around it. Then why an electric iron connecting cable does not attract barb iron objects when electric current is switched on through it?
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Answer 1

Only open wire cause magnetic field. Close wire doesn't .

Answer 2

The Current carrying wire is usually straight and also the current through it is also low.

The magnetic field produced by a straight  current carrying wire is given by

B=μI/2πr

This magnetic field is not enough to attract nearby objects.