91Ó°ÊÓ

Electric charge is the property of an elementary particle which gives rise to the electric force between the two elementary particles.

It is of two kinds, positive and negative. The value of the basic unit of charge present on an electron or proton is \(e = 1.602 \times {10^{ - 19}}\;{\rm{C}}\).

The total charge on a body is always quantized, i.e., it is the integral multiple of the basic unit of charge.

\(q = ne\)

Here, n is an integer.

Mass of the person is, \(M = 75\;{\rm{kg}}\)

Each water molecule has two atoms of hydrogen and one atom of oxygen. The atomic mass of oxygen is 8 and that of hydrogen is 1. So, the atomic mass of the water is 18.

One molecule of water contains 10 electrons and 10 protons. Consider only protons to estimate the amount of positive charge.

Charge on each proton is, \(q = 1.602 \times {10^{ - 19}}\;{\rm{C}}\)

Thus, the total positive charge in each water molecule is,

\(\begin{aligned}{c}q' = 10q\\ = 10 \times 1.602 \times {10^{ - 19}}\;{\rm{C}}\\ = 1.602 \times {\rm{1}}{{\rm{0}}^{ - 18}}\;{\rm{C}}\end{aligned}\)

The number of molecules in one mole of water is \(6.02 \times {10^{23}}\;{\rm{molecules}}\).

Mass of one mole of water molecules is,\(m = 18\;{\rm{g}} = 18 \times {\rm{1}}{{\rm{0}}^{ - 3}}\;{\rm{kg}}\)

So, you can say that there are \(6.02 \times {10^{23}}\;{\rm{molecules}}\) in \(18 \times {\rm{1}}{{\rm{0}}^{ - 3}}\;{\rm{kg}}\). So, 1 kg of water contains \(\frac{{6.02 \times {{10}^{23}}}}{{18 \times {\rm{1}}{{\rm{0}}^{ - 3}}}}\;{\rm{molecules}}\).

Since the human body is mostly made out of water. Thus, the number of water molecules in a 75 kg person is,

\(\begin{aligned}{c}N = 75 \times \frac{{6.02 \times {{10}^{23}}}}{{18 \times {\rm{1}}{{\rm{0}}^{ - 3}}}}\;{\rm{molecules}}\\ = 25.08 \times {10^{26}}\;{\rm{molecules}}\end{aligned}\)

The total amount of positive charge in a 75 kg person is equal to the number of water molecules in the person’s body times the charge contained in each water molecule, i.e.,

\(\begin{aligned}{c}Q = Nq'\\ = 25.08 \times {10^{26}} \times 1.602 \times {\rm{1}}{{\rm{0}}^{ - 18}}\;{\rm{C}}\\ = 4{\rm{0}}{\rm{.17}} \times {\rm{1}}{{\rm{0}}^8}\;{\rm{C}}\\ = 4.0 \times {\rm{1}}{{\rm{0}}^9}\;{\rm{C}}\end{aligned}\)

Thus, the total amount of positive charge in a 75-kg person is \(4.0 \times {\rm{1}}{{\rm{0}}^9}\;{\rm{C}}\).