Confusion about charging a conductor positively or negatively

Question

In my books,Principle of Physics(Grade XI),it shows the process of charging a conductor positively or negatively by induction.At the last picture,when the charge is completed it says'The positive or negative charge left in a conductor spread unifromly across the conductor.Hence the conductor is negatively/positively charged depending on case'.

My questions are:

1. How can body be charge positively?I know that some electrons in surface can leave out but how can the all the electrons,those in the middle also,leave the conductor and make it positively charged?Atleast the picture in my books shows a long pipe conductor with only + charge all across the surface

2. How can body be charged negatively? Where do the protons go? Please help !!

Answer 1

Charging an object positively or negatively is almost always done by removing or adding electrons. The nuclei stay - if you take electrons away the remaining ones will redistribute - in the way that soldiers would step into the gap in the line made when their comrades fell during battle. But the electrons can't be both in the new place and the old place - and as they move around, the leave, on average, a slight net positive charge everywhere.

The opposite happens with negative charge - slightly too many electrons will "crowd" each other, so they are a little closer together and there are slightly more electrons than protons for a net negative charge.

Note - the number of surplus electrons needed is quite tiny. If you take a 10 cm radius sphere and charge it to 1000 V, we can compute the number of electrons involved:

We start with the charge needed: we know that

$$V = \frac{Q}{4\pi\epsilon_0 r}$$

So we find $Q = 1.1\times 10^{-8} C$, which corresponds to roughly $7\times 10^{10}$ electrons. If your sphere is made of 1 mole of copper (63.5 gram - pretty light) then you have approximately 1 extra electron for every $10^{13}$ atoms.

To get a sense of how small that is - if every human (man, woman and child) on the planet had 1400 dollars, the extra electrons needed in the above example is equivalent to giving one person (out of the 7 billion) one extra dollar.