Solveeit Logo
Login

Question

Question: If \({{10}^{+9}}\) electrons move out of a body to another body every second, how much time is requi...

If 10+9{{10}^{+9}} electrons move out of a body to another body every second, how much time is required to get a total charge of 1C1C on the other body?

Explanation

Solution

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 1C1C.

Formula used:
Charge Quantization: Q=neQ=ne
Where QQ is the net charge, nn is the number of electrons and ee 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{{10}^{+9}}electrons per second. Therefore, the charge that is emitted by the body is given by Q=neQ=ne. Here QQ is the net charge, nn is the number of electrons and ee is the charge on an electron(1.6×10−19C1.6\times {{10}^{-19}}C).
Q=(10+9)(1.6×10−19C) ⇒Q=1.6×10−10CQ=({{10}^{+9}})(1.6\times {{10}^{-19}}C) \\\ \Rightarrow Q=1.6\times {{10}^{-10}}C

Accordingly, we can say that the body emits 1.6×10−10C1.6\times {{10}^{-10}}C charge per second.Now, we need to calculate how much time the body takes to emit 1C1C charge.Therefore, we can write the equation as
Qtotal=Q×t ⇒t=QtotalQ{{Q}_{total}}=Q\times t \\\ \Rightarrow t=\dfrac{{{Q}_{total}}}{Q}
Where Qtotal{{Q}_{total}} is the charge of 1C1C and QQ is the net charge we calculated.
t=11.6×10−10 ⇒t=0.625×1010st=\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
[60sec⁡=1min⁡ 60min⁡=1hr 24hr=1day 365days=1 year]\left[ 60\sec =1\min \\\ 60\min =1hr \\\ 24hr=1day \\\ 365days=1\,year\right]
Therefore,
t=0.625×101060×60×24×365 ∴t=198.18 years≈200 years 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 1C1C charge from a body to another will be approximately 200 years200\,years.

Note: It is very important to note that the charge on one electron is 1.6×10−19C1.6\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.