Why batteries don't exhibit static electricity? If I correctly understood how batteries work: once they are connected to a circuit, there is a chemical reaction inside that separates electrons from atoms, moving the positive ions to one terminal and the electrons to the other terminal. When the battery is removed, the process stops but some positive charges remain on the positive rod (terminal) and some negative charges on the negative terminal.
If there are charges left in any of the terminals, why approaching one terminal from a piece of paper or an electroscope doesn't show any kind of static electricity?
 A: 
If there are charges left in any of the terminals, why approaching one terminal from a piece of paper or an electroscope doesn't show any kind of static electricity ?

It is simply a matter of scale. A battery would have 1.5 V to 12 V worth of static electricity, but the minimum detection threshold for a human is about 3 kV of static electricity. So there is static electricity there, but just not an amount that we can notice.
A: Although only a ‘rule of thumb’ current electricity deals with small voltages (~V) and large currents (~A) whereas electrostatics deals with comparatively large voltage (~kV) but comparatively small ‘currents’ (~pA). Obviously there is overlap but note that charging a rod by rubbing it can produce voltages in excess of 10 kV but the amount of stored charged and hence the resulting currents are very small.  A leaf type electroscope only shows a deflection with voltages in excess of hundreds of volts.
In terms of cells connecting enough of them in series can produce a lethal voltage and charging a capacitor in the form of a Leyden jar from a Whimshurst machine or even an electrophorus can store sufficient charge to produce a lethal electric current.
Historically it took time for scientists that both branches were manifestations of the same thing - electricity.
