Question

A conductor has $14.4 \times {10^{ - 19}}C$ positive charge. The conductor has (charge on an electron is $1.6 \times {10^{ - 19}}C$ )
A. $9$ Electrons in excess
B. $27$ Electrons in excess
C. $9$ Electrons in short
D. $27$ Electrons in short

Answer 1

In order to solve this question we should understand about quantization of charges. Electric charge is the fundamental property of all matter which is the cause of electricity and magnetism and any matter or body having total number of charge inside it is always quantized with the charge on electron and if a substance has more positive charge on it means body has shortage of electron or if body has more negative charge it means body have shortage of positive charges, we will use the concept of quantization to solve this problem.

Formula used:
If $Q$ is the total charge in a body and $e$ is the electron charge and $n$ is the total number of charges in it then, $Q = ne$.

Complete step by step answer:
According to the question, we have given that the total positive charge in the conductor is $Q = 14.4 \times {10^{ - 19}}C$ which means the conductor is short of electrons. Also, let $n$ be the number of electrons then we have,
$e = 1.6 \times {10^{ - 19}}C$
Using formula of quantization formula,
$Q = ne$
We get,
$14.4 \times {10^{ - 19}} = n(1.6 \times {10^{ - 19}})$
$\therefore n = 9$
So, there are nine electrons which are in shortage as compared to positive charges.

Hence, the correct option is C.

Note: It should be remembered that, among the fundamental property of matter as charge, charge has only two polarities either positive or negative and proton has same amount of charge as amount of charge on electron but the polarity of electron is negative whereas the polarity on proton is positive.