Calculating the Charge from Electrons Added to a Neutral Dielectric

Understanding the relationship between the number of electrons and the resulting charge is a fundamental concept in physics. Let's explore how to calculate the charge when a specific number of electrons is added to a neutral dielectric material.

A neutral dielectric means the material initially has no net charge. Adding a large number of electrons to this material will result in a negative charge. The key to solving this problem is knowing the charge of a single electron and performing a straightforward multiplication.

The Electron Charge

The charge of a single electron is a standard value in physics, denoted by ( e ). The value of the electron charge is:

[text{1 electron charge} 1.60218 times 10^{-19} text{ Coulombs}]

Calculating the Total Charge

Let's consider the scenario where 18.75 × 1018 electrons are added to a neutral dielectric. To find the total charge, we can follow these steps:

Identify the number of electrons being added: ( N 18.75 times 10^{18} ) electrons. Identify the charge of a single electron: ( e 1.60218 times 10^{-19} ) Coulombs. Multiply the number of electrons by the charge of a single electron to get the total charge: [text{Total charge} N times e (18.75 times 10^{18}) times (1.60218 times 10^{-19}) text{ Coulombs}]

(18.75 times 10^{18} times 1.60218 times 10^{-19} 3.004 text{ Coulombs}

This calculation confirms that when 18.75 × 1018 electrons are added to a neutral dielectric, the resulting charge is approximately 3.004 Coulombs. This positive result is due to the consistent negative charge of the electrons.

Understanding the Context

The scenario given does not explicitly mention the context, such as whether the charge is being added to a capacitor or if a dielectric is being introduced between plates. However, it is important to note that a dielectric material can affect the capacitance of a capacitor, not the total charge. Adding a dielectric material between the plates of a capacitor reduces the electric field between the plates but does not change the total charge.

The total charge in a system remains conserved unless charge is added or removed from the system. In this specific case, the addition of 18.75 × 1018 electrons will inherently impart a negative charge of 3.004 Coulombs to the dielectric material.

Conclusion

In summary, the process of calculating the charge from the number of electrons added to a neutral dielectric involves a simple multiplication. The total charge is a direct result of the number of electrons and their individual charges. This concept is foundational in understanding electrostatics and is crucial for applications in various scientific and engineering fields.

If you have any other specific questions or need further clarification, feel free to ask!