I am teaching high school physics and our textbook says that "If a charged rod is brought close to the electroscope and the cap is earthed momentarily, the electroscope is left with the opposite to that on the rod."
And the usual explanations for it goes as this:
If a negatively charged rod is brought close to the cap of the electroscope, electrons are repelled to the leaves, leaving the cap positive. If the cap is earthed, by a finger say, the electrons run away to earth. If the finger is removed first, followed by the rod, the electroscope is left positively charged.
The question asked: How do the electrons overcome the repulsion of the negative rod to run to earth?
Best Answer
The negative charges will want to get as far away from each other as possible. Since our bodies are fairly good conductors, this is fairly easy for the negative charges to move towards ground to achieve this. The repulsion of the negative charges on the rod is just not enough to completely contain all of the negative charge in the electroscope. Negative charges in the tip are much closer to each other than they are to the rod, so this repulsion will win initially to create an overall net positive charge on the electroscope.
If this is unconvincing you could go this route instead. To get a net positive charge on the electroscope we do not need to remove much negative charge from the electroscope. Even though the diagram shows positive charge at the tip before we touch it, this does not mean it is devoid of negative charge. It just means there is a net positive charge there. So when we touch the tip there will be some negative charges where the negative rod will actually aid in pushing these charges to ground through the finger. This is enough to give the electroscope a net positive charge since some negative charge has left it.