Question is in the image. Calculate final charge distribution and explain step by step

To calculate the final charge distribution in a system, we need to understand the principles of electrostatics and how charges interact with one another. Let's break this down step by step, using a hypothetical scenario where we have two conductive spheres that are initially uncharged and then brought into contact with each other. Afterward, they are separated, and we want to find the final charge distribution on each sphere.

Initial Setup

Imagine we have two identical conductive spheres, Sphere A and Sphere B. Initially, both spheres have no charge, meaning they are electrically neutral. When we bring them into contact, the charges can redistribute between the two spheres.

Step 1: Bringing the Spheres into Contact

When the two spheres touch, electrons can move freely between them. Since both spheres are identical and initially neutral, the total charge before contact is zero. When they touch, the electrons will redistribute evenly between the two spheres due to their identical nature and the principle of charge conservation.

Step 2: Charge Redistribution

Let’s say we introduce a positive charge of +Q to Sphere A before bringing it into contact with Sphere B. The total charge in the system is now +Q (from Sphere A) and 0 (from Sphere B), giving a total of +Q. When the spheres touch, the positive charge will attract electrons from Sphere B, causing some electrons to move from Sphere B to Sphere A until the potential on both spheres equalizes.

Step 3: Final Charge Distribution

After the spheres are separated, they will each have a charge of +Q/2. This is because the total charge of +Q has been evenly distributed between the two identical spheres. Thus, Sphere A will have +Q/2 and Sphere B will also have +Q/2.

Key Principles at Work

• Conservation of Charge: The total charge in an isolated system remains constant. In our case, the total charge before and after contact remains +Q.
• Equal Potential: When two conductors are in contact, they will reach the same electric potential, leading to an even distribution of charge.
• Identical Conductors: Since both spheres are identical, the charge will distribute evenly between them.

Example Scenario

Let’s say we start with Sphere A having a charge of +10 µC and Sphere B being neutral. When they touch, the total charge is +10 µC. After separation, each sphere will have a charge of +5 µC. This illustrates how charge redistribution occurs in a simple system.

Final Thoughts

Understanding charge distribution is crucial in electrostatics, as it helps us predict how charges will behave in various configurations. By applying the principles of conservation of charge and equal potential, we can analyze more complex systems involving multiple charges and conductors. If you have any specific scenarios or additional questions, feel free to ask!