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A cup contains 250g of water. Find the total positive charge present in the cup of water.
A. $1.34 \times {10^{19}}{\rm{C}}$
B. $1.34 \times {10^7}{\rm{C}}$
C. $2.43 \times \;{10^{19}}{\rm{C}}$
D. $2.43 \times \;{10^7}{\rm{C}}$

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Last updated date: 21st Jun 2024
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Answer
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Hint: Electric charge is the physical property of matter that causes it to experience a force under the influence of an electromagnetic field. There are two types of charges, namely, positive and negative called protons and electrons respectively. To calculate the total charge, we need first to find the charge present on 1 electron. That is, we have to multiply the charge present on an electron with the total number of electrons.
The formula used to calculate the total charge is given below:
${\rm{Q}}\;{\rm{ = n}}{\rm{.e}}$
Where $Q$ is the charge, $n$ is the number of electrons and e is the charge on an electron.

Complete step by step answer:
According to the question:
Mass of water is $ = 250{\rm{g}}$
We know that the mass of water $ = 18{\rm{g}}$
Therefore the no. of molecules in $18{\rm{g}}$ of water $ = 6.02 \times {10^{23}}$
$ \Rightarrow $ The number of molecules in one cup of water is ($n$) $ = \;\dfrac{{250}}{{18}} \times 6.02 \times {10^{23}}\; = \;83.61 \times {10^{23}}$
Also, each molecule of water contains two hydrogen, and one is oxygen, i.e. 10 electrons and 10 protons.
Therefore the total positive charge present in one cup of water;
$ \Rightarrow {\rm{Q}} = \;83.61 \times {10^{23}}\; \times 10 \times 1.6 \times {10^{ - 19}}{\rm{C}}$
$ \Rightarrow {\rm{Q = }}\;{\rm{1}}{\rm{.34}} \times {\rm{1}}{{\rm{0}}^7}{\rm{C}}$ .

Hence the correct option is (B).

Note:
Always remember that the value of the charge $({\rm{e}} = 1.6 \times {10^{ - 19}}{\rm{C)}}$. The SI unit of electric charge is coulombs (C). Another unit of electric charge is Ampere-second (A-s). Electric charge is always conserved. This means the sum of protons and electrons, i.e. the net charge of an isolated system remains the same. Static electric charges produce electric fields. On the other hand, moving charges produce magnetic fields.