Electrostatic Potential And Capacitance

Understanding the Problem:

• Three point charges are arranged linearly: , , and
• Equal spacing between consecutive charges
• Find the ratio for zero net electric potential energy

Key Formulae:

• Coulomb's law: where
• Potential energy between two charges:

System Configuration:

• Charge arrangement: (left), (center), (right)
• Distances: to , to , to

Potential Energy Calculation:

Total potential energy has three components:

1. Between and :

2. Between and :

3. Between and :

Total Potential Energy:

Condition for Zero Energy:

Set :

Simplify:

Non-Trivial Solution:

Final Answer: The required ratio is .