📘 Chapter 22: Electric Potential Energy of a System of Two Point Charges (Class XII)

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🔷 1. Introduction

In electrostatics, the concept of electric potential energy helps us understand how energy is stored in a system of charges due to their positions.

For a system of two point charges, this energy represents the work required to assemble the charges from infinity to a given configuration.

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🔷 2. Definition of Electric Potential Energy

Electric potential energy is defined as the work done in bringing charges from infinity to their positions without acceleration.

For two point charges:

U = (1 / 4πε₀) (q₁q₂ / r)

Where:

• U = potential energy
• q₁, q₂ = charges
• r = distance between them

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📦 3. Important Results (Must Remember)

• Potential energy: U = (1/4πε₀)(q₁q₂/r)
• Scalar quantity
• Unit: Joule (J)
• Reference: U = 0 at infinity
• Depends on distance and nature of charges

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🔷 4. Nature of Potential Energy

• Like charges (both + or both −): U is positive
• Unlike charges: U is negative

This indicates:

• Positive U → repulsive system
• Negative U → attractive system

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🔷 5. Variation with Distance

Potential energy varies inversely with distance:

U ∝ 1/r

• As r increases → U decreases
• At r → ∞ → U → 0

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🔷 6. Physical Interpretation

Electric potential energy represents the stored energy due to interaction between charges.

It tells us whether the system tends to:

• Move apart (repulsion)
• Come together (attraction)

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🔷 7. Work Done in Bringing Charges

Work done in assembling system:

W = U

Thus, potential energy equals work required to build the system.

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🔷 8. Zero Potential Energy Reference

We assume:

U = 0 at infinite separation

All calculations are made relative to this reference.

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🧠 9. Solved Numerical Problems

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🔹 Q1

Find potential energy of two charges 2μC and 3μC separated by 0.5 m.

Solution:

U = k q₁q₂ / r

= 9×10⁹ × (2×10⁻⁶ × 3×10⁻⁶) / 0.5

U = 0.108 J

Answer: 0.108 Joule

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🔹 Q2

What is sign of energy for opposite charges?

Answer:

Negative

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🔹 Q3

What happens to energy when distance increases?

Answer:

Energy decreases toward zero.

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🔹 Q4

Why is potential energy positive for like charges?

Answer:

Because work is required against repulsive force.

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🔹 Q5

What is potential energy at infinite separation?

Answer:

Zero

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🔷 10. Advanced Conceptual Insight

Electric potential energy is a key concept in understanding energy conservation in electrostatics. It forms the basis for studying systems of multiple charges and electric potential energy density.

It is also widely used in atomic physics and molecular interactions.

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🔷 11. Applications

• Energy stored in charge systems
• Molecular bonding
• Capacitor energy analysis
• Electrostatic stability studies

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🔷 12. Summary

Electric potential energy of two point charges depends on their magnitudes, separation, and nature. It represents the work required to assemble the system and plays a crucial role in electrostatics.

✨ End of Chapter 22: Electric Potential Energy ✨