Use 'magnetically' in discussions about physics to describe magnetic interactions or effects. The particles are magnetically bound within the material.
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Physical Movement
'Magnetically' can explain movement caused by magnetic forces, not physical pushing or pulling. The iron filings moved magnetically towards the magnet.
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Metallic Interaction
It's mostly used when metals or materials with magnetic properties react with a magnet. The door latch held magnetically, without a key.