Numerical-1

Q . If 10^9 electrons move out of a body to another body every second, how much time is required to get a total charge of 1 C on the other body?

Solution :

In one second 10^9 electrons move out of the body. Therefore

the charge given out in one second is 1.6 × 10^–19 × 10^9 C = 1.6 × 10–^10 C.

The time required to accumulate a charge of 1 C can then be estimated to be 1 C ÷ (1.6 × 10^–10 C/s) = 6.25 × 10^9 s = 6.25 × 10^9 ÷ (365 × 24 × 3600) years = 198 years. 

Thus to collect a charge of one coulomb, from a body from which 10^9 electrons move out every second, we will need approximately 200 years. 

One coulomb is, therefore, a very large unit for many practical purposes.

It is, however, also important to know what is roughly the number of

electrons contained in a piece of one cubic centimetre of a material.

A cubic piece of copper of side 1 cm contains about 2.5 × 10^24

electrons.

Numerical-2

Q.  How much positive and negative charge is there in a cup of water?

Solution : 

Let us assume that the mass of one cup of water is 250 g. The molecular mass of water is 18g. Thus, one mole (= 6.02 × 10^23 molecules) of water is 18 g. 

Therefore the number of molecules in one cup of water is (250/18) × 6.02 × 10^23.

Each molecule of water contains two hydrogen atoms and one oxygen atom, i.e., 10 electrons and 10 protons. Hence the total positive and total negative charge has the same magnitude. 

It is equal to

(250/18) × 6.02 × 10^23 × 10 × 1.6 × 10^–19 C = 1.34 × 10^7 C.