Combination sink/source in one object

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nomadreid
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Is there any phenomenon (in physics: no wisecracks about human interactions ) in which A is attracted from further out to B until it gets close to B, whereupon A is repelled from B? (Sort of the opposite to the switch between the electromagnetic repulsion being overpowered by the strong force in tunneling.)?
 
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Thank you, Orodruin. I will have to do a bit of research to find out precisely how this works, but you have put me on the right path.