Question

What is the total charge on 75 kg of electrons?

Answer 1

Hint: The number of electrons equals the total mass by the mass of each electron. The total charge equals the number of electrons times the net charge on an electron. We know the value of the mass of the electron and the charge on each electron, thus, using the same, we will compute the total charge.
Formulae used:
\[n=\dfrac{M}{m}\]
\[q=ne\]

Complete answer:
Firstly we will compute the total number of electrons that form a total weight of 75 kg. The total number of electrons is given by the formula as follows.
The number of electrons is equal to the total mass by the mass of each electron.
We know the mass of each electron, that is, \[m=9.1\times {{10}^{-31}}kg\]
The total mass of the electrons is, \[M=75kg\]
Thus, the total number of electrons is computed as follows.
\[n=\dfrac{M}{m}\]
Where M is the total mass and m is the mass of each electron.
Substitute the values in the above formula.
\[n=\dfrac{75}{9.1\times {{10}^{-31}}}\]
Continue further computation.
\[\begin{align}
  & n=\dfrac{75}{9.1}\times {{10}^{31}} \\
 & \therefore n=\dfrac{25}{3}\times {{10}^{31}} \\
\end{align}\]
Now, we will compute the total charge on 75 kg of electrons as follows.
\[q=ne\]
Where q is the charge on the electron, n is the total number of electrons and e is the charge on an electron.
The charge on electron is, \[e=-1.6\times {{10}^{-19}}C\]
\[q=\dfrac{25}{3}\times {{10}^{31}}\times (-1.6\times {{10}^{-19}})\]
Continue further computation.
\[\begin{align}
  & q=-\dfrac{25}{3}\times 1.6\times {{10}^{-19}}\times {{10}^{31}} \\
 & \Rightarrow q=-13.33\times {{10}^{12}} \\
 & \therefore q=-1.33\times {{10}^{13}}C \\
\end{align}\]
Thus, the charge is \[-1.33\times {{10}^{13}}C\].
\[\therefore \] The total charge on 75 kg of electrons is \[-1.33\times {{10}^{13}}C\]

Note:
In this question, the total charge on 75 kg of electrons is asked, even they can ask for the total charge on 75 kg of protons. In that case, as the mass of a proton is different from that of an electron, thus, the mass changes and the sign on the charge gets reversed.