A conductor has 14.4 × 10⁻¹⁹ C positive charge the conductor has :- (a) 9 electron in excess (b) 27

A conductor has 14.4 × 10⁻¹⁹ C positive charge the conductor has :-
(a) 9 electron in excess
(b) 27 electron in excess
(c) 9 electron in short
(d) 27 electron in short
*Understanding Charge and Electrons in a Conductor* ⚡️
In this video, we’ll explore a problem related to the charge on a conductor and its relationship with the number of electrons. We’ll calculate how many electrons are in excess or short in a conductor when a specific charge is given. Let’s break it down for both JEE and NEET aspirants!
*Problem Overview* 💡:
A conductor carries a positive charge of **14.4 × 10⁻¹⁹ C**. The task is to determine whether the conductor has an excess or shortage of electrons, and if so, how many.
*Key Concept* 🔍:
**Charge of an Electron**: The charge on a single electron is approximately **\( e = 1.6 \times 10^{-19} \) C**.
**Excess or Shortage of Electrons**:
If a conductor has a positive charge, it means it has lost electrons (electron deficit).
If a conductor has a negative charge, it means it has gained electrons (electron excess).
*Step-by-Step Solution* 🧠:
1. **Charge on the Conductor**: The total positive charge on the conductor is **14.4 × 10⁻¹⁹ C**.
2. **Charge of a Single Electron**: The charge on one electron is **1.6 × 10⁻¹⁹ C**.
3. **Number of Electrons**:
To calculate how many electrons are involved, divide the total charge by the charge of one electron:
\[
\text{Number of electrons} = \frac{\text{Total charge}}{\text{Charge of one electron}} = \frac{14.4 \times 10^{-19}}{1.6 \times 10^{-19}} = 9
\]
*Conclusion* 🔑:
Since the charge is **positive**, the conductor must be **short of 9 electrons**. Hence, the correct answer is **(c) 9 electrons in short**.
*Important Insights* 📚:
This problem highlights the relationship between the charge on a conductor and the number of electrons involved.
It emphasizes the importance of understanding the concept of *charge conservation* and how electrons play a crucial role in charge transfer.
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