Electrostatic force - charges jumping between objects

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jssutton11
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So I have this homework question that I answered already but still don't understand why the answer is correct.

A positively charged ball is brought close to an electrically neutral isolated conductor. The conductor is then grounded while the ball is kept close. Is the conductor charged positively, charged negatively, or neutral in each of the following cases?
(a) The ball is first taken away and then the ground connection is removed.
(b) The ground connection is first removed and then the ball is taken away.

I understand that in (a) the conductor will be neutral because the grounding effect causes electrons to go straight to the ground. But (b) I don't understand. The answer says that the conductor will be charged negatively, but I thought that when two charged objects are close or touch each other, the charge is shared between them. Or maybe that charge is only shared when the objects touch. Either way, I don't understand why the positively charged ball would make the conductor negative.
 
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your making it complicated. its simple. stop thinking about equations and just ask yourself what an electron in the ground would do.
 
An electron would go to a positively charged object, thus making that object it less positive. But would electrons just continue flowing from the conductor into the ball until the ball was negative?
 
why would electrons flow into the ball if they arent touching?