CGS vs. SI Units for Electric Charge
In physics, we use different systems of units to measure quantities like electric charge. The question involves the CGS (Centimeter-Gram-Second) system, which has units like the electrostatic unit (esu) and the electromagnetic unit (emu) for charge. It also refers to the Coulomb (C), which is the standard unit of charge in the SI (International System of Units). Understanding the relationship between these units is key.
Charge Unit Ratio: emu, esu, and the Speed of Light
The question states a fundamental relationship in electromagnetism: the ratio of the magnitude 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, denoted by '$c$'.
Mathematically, this relationship indicates:
$ \frac{\text{1 emu of charge}}{\text{1 esu of charge}} = c $
Given the approximate value of the speed of light in a vacuum as '$c \approx 3 \times 10^8 \text{ m/s}$', this highlights the connection between electrical units and the speed of light. This connection arises from the fundamental constants and definitions used in the CGS and SI systems.
Calculating Coulomb Equivalent in Electrostatic Units (esu)
The core task is to determine the equivalent charge in electrostatic units (esu) for $1$ Coulomb (C). The Coulomb is the standard unit of charge within the SI system.
Based on established physical principles and definitions that relate the CGS and SI systems, a specific conversion factor exists between the Coulomb and the electrostatic unit (esu).
The standard conversion factor is:
$ 1 \text{ Coulomb (C)} = 3 \times 10^9 \text{ electrostatic units (esu)} $
Step-by-Step Conversion
To perform the conversion from Coulomb to esu for $1$ Coulomb, we apply this established factor:
- We start with the quantity we need to convert: $1 \text{ C}$.
- We use the conversion factor that relates Coulombs to esu: $ \frac{3 \times 10^9 \text{ esu}}{1 \text{ C}} $.
- Multiply the quantity by the conversion factor: $ 1 \text{ C} \times \frac{3 \times 10^9 \text{ esu}}{1 \text{ C}} $.
- The unit 'C' cancels out during the multiplication.
- This leaves us with the result in the desired unit: $ 3 \times 10^9 \text{ esu} $.
Thus, $1$ Coulomb of electric charge is equivalent to $3 \times 10^9$ electrostatic units (esu).
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?
- 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:
- 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?
