Suppose every second 1016 electrons come out of a body and move to another body, then the time is required to get a total charge of 3.2 C on the other body is:
Charge Accumulation Time Calculation
This problem requires us to calculate the time needed for a specific amount of charge to accumulate on a body, given the rate at which electrons are transferred. It involves fundamental concepts of electric charge and the properties of electrons.
Electron Charge and Quantity
The total electric charge on a body is quantized, meaning it exists in discrete multiples of the elementary charge. The elementary charge is the magnitude of the charge of a single electron or proton. For an electron, this value is negative.
- The charge of a single electron, denoted as \(\text{e}\), is approximately \(1.6 \times 10^{-19}\) Coulombs (C).
- The total charge, \(\text{Q}\), accumulated on a body due to the transfer of \(\text{n}\) electrons is given by the formula: \(\text{Q} = \text{n} \times \text{e}\).
Given Information
From the question, we have the following data:
- Rate of electron flow: \(10^{16}\) electrons per second. This means every second, \(10^{16}\) electrons are transferred.
- Total charge (\(\text{Q}\)) to be accumulated: \(3.2\) C.
Calculating the Total Number of Electrons
Before we can determine the time, we need to find out how many total electrons are required to form a charge of \(3.2\) C. Using the formula \(\text{Q} = \text{n} \times \text{e}\), we can solve for \(\text{n}\):
\(\text{n} = \frac{\text{Q}}{\text{e}}\)
Substitute the given total charge and the charge of a single electron:
\(\text{n} = \frac{3.2 \, \text{C}}{1.6 \times 10^{-19} \, \text{C/electron}}\)
Performing the division:
\(\text{n} = \frac{3.2}{1.6} \times 10^{-(-19)} \, \text{electrons}\)
\(\text{n} = 2 \times 10^{19} \, \text{electrons}\)
Therefore, a total of \(2 \times 10^{19}\) electrons are needed to accumulate a charge of \(3.2\) C.
Determining the Required Time
Now that we know the total number of electrons that need to be transferred and the rate at which they are being transferred per second, we can calculate the total time required:
\(\text{Time (t)} = \frac{\text{Total number of electrons}}{\text{Number of electrons transferred per second}}\)
Substitute the calculated total number of electrons and the given rate of electron flow:
\(\text{t} = \frac{2 \times 10^{19} \, \text{electrons}}{10^{16} \, \text{electrons/second}}\)
To simplify, we subtract the exponents of 10:
\(\text{t} = 2 \times 10^{(19-16)} \, \text{seconds}\)
\(\text{t} = 2 \times 10^3 \, \text{seconds}\)
\(\text{t} = 2000 \, \text{seconds}\)
Conclusion on Time Required
Based on our calculations, the time required to accumulate a total charge of \(3.2\) C on the other body, given that \(10^{16}\) electrons are transferred every second, is \(2000\) seconds.
Important Questions from Electric Charge
Which of the following expressions correctly represents the SI unit of electric charge, the Coulomb ($C$), in terms of other fundamental or derived SI units?
- An object is found to have a net negative charge of $-5 \text{ nC}$. How many excess electrons are present on the object? (Given: elementary charge $e = 1.6 \times 10^{-19} \text{ C}$)
- A metallic sphere, initially possessing a positive electric potential relative to the Earth, is connected to the Earth by a conducting wire. Which of the following accurately describes the primary charge movement that occurs until equilibrium is reached?
Two point charges, $Q_1 = +3 \mu C$ and $Q_2 = -8 \mu C$, are placed at a certain distance apart. They attract each other with a force of $48 N$. If each charge is given an additional charge of $+6 \mu C$, what will be the magnitude and nature of the new force between them?
- In the CGS system of units, the ratio of the electromagnetic unit (emu) of charge to the electrostatic unit (esu) of charge is numerically equivalent to the speed of light in a vacuum, '$c$'. Considering the value of '$c \approx 3 \times 10^8 \text{ m/s}$', what is the equivalent charge in electrostatic units (esu) for '$1$ Coulomb'?
