Question

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 \[1C\] on the other body?

Answer 1

Hint: In order to find the solution to the above question, we will be using the concept of charge quantization and the conservation of charge. We will calculate the charge transferred per seconds and then find the time to transfer charge of $1C$.

Formula used:
Charge Quantization: $Q=ne$
Where $Q$ is the net charge, $n$ is the number of electrons and $e$ is the charge on an electron.

Complete step by step answer:
First of all we will be writing down all the data which is provided in the question. The body emits ${{10}^{+9}}$electrons per second. Therefore, the charge that is emitted by the body is given by $Q=ne$. Here $Q$ is the net charge, $n$ is the number of electrons and $e$ is the charge on an electron($1.6\times {{10}^{-19}}C$).
$Q=({{10}^{+9}})(1.6\times {{10}^{-19}}C) \\
\Rightarrow Q=1.6\times {{10}^{-10}}C $

Accordingly, we can say that the body emits $1.6\times {{10}^{-10}}C$ charge per second.Now, we need to calculate how much time the body takes to emit \[1C\] charge.Therefore, we can write the equation as
${{Q}_{total}}=Q\times t \\
\Rightarrow t=\dfrac{{{Q}_{total}}}{Q} $
Where ${{Q}_{total}}$ is the charge of \[1C\] and $Q$ is the net charge we calculated.
$t=\dfrac{1}{1.6\times {{10}^{-10}}} \\
\Rightarrow t=0.625\times {{10}^{10}}s $
As the power is very large, we will convert this value into years. We already know that
$\left[ 60\sec =1\min \\
60\min =1hr \\
24hr=1day \\
365days=1\,year\right]$
Therefore,
$t=\dfrac{0.625\times {{10}^{10}}}{60\times 60\times 24\times 365} \\
\therefore t=198.18\,years\approx 200\,years \\ $
Hence, the time required to transfer $1C$ charge from a body to another will be approximately $200\,years$.

Note:It is very important to note that the charge on one electron is $1.6\times {{10}^{-19}}C$ and is always quantized. Also, special care needs to be taken while calculating the time and converting its units according to our requirement.