How do magnetic fields around connected conductive materials take shape?

How do magnetic fields around connected conductive materials take shape?
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I think that while the current supplied by the wire is flowing through the metal balls they will generate a magnetic field in the same way a field surrounds a wire with electricity flowing through it. The field collapses when the voltage is removed and neither the wire nor the balls will be magnetized. I imagine because the current will pass through them as a group, that in the same way it passes between atoms in a wire their magnetism will not repel them.
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