📘 Chapter 10: Electric Dipole (Class XII)

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🔷 1. Introduction

An electric dipole is one of the most fundamental charge configurations in electrostatics. It consists of two equal and opposite charges separated by a small distance. Dipoles are widely found in nature, especially in molecules, and play a crucial role in understanding electric fields and potentials.

The concept of dipole bridges simple point charges and complex charge distributions.

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🔷 2. Definition of Electric Dipole

An electric dipole consists of two charges:

• +q (positive charge)
• −q (negative charge)

separated by a distance 2a.

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🔷 3. Dipole Moment

The strength of a dipole is measured by its dipole moment.

p = q × 2a

Vector form:

p⃗ = q (2a) r̂

Direction:

From negative charge to positive charge

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📦 4. Important Results (Must Remember)

• Dipole moment: p = q × 2a
• Direction: − → +
• Unit: Coulomb-meter (C·m)
• Vector quantity
• Represents strength of dipole

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🔷 5. Electric Field Due to Dipole

There are two important cases:

(a) Axial Line

E = (1 / 4πε₀) (2p / r³)

Direction: along dipole moment

(b) Equatorial Line

E = (1 / 4πε₀) (p / r³)

Direction: opposite to dipole moment

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🔷 6. Nature of Dipole Field

• Field decreases as 1/r³ (faster than point charge)
• Non-uniform field
• Curved field lines
• Strong near charges, weak at large distances

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🔷 7. Torque on Electric Dipole

When a dipole is placed in an external electric field, it experiences a torque.

τ = pE sinθ

Where θ is angle between dipole moment and electric field.

• Dipole tends to align with electric field
• Stable equilibrium at θ = 0°

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🔷 8. Potential Energy of Dipole

Potential energy in electric field:

U = −pE cosθ

Minimum energy at θ = 0° (aligned with field)

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🔷 9. Electric Field Lines of Dipole

• Start from positive charge and end at negative charge
• Symmetrical pattern
• Curved lines indicating non-uniform field

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🧠 10. Solved Numerical Problems

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🔹 Q1

Find dipole moment of charges ±2 μC separated by 4 cm.

Solution:

p = q × 2a = 2×10⁻⁶ × 0.04

p = 8×10⁻⁸ C·m

Answer: 8×10⁻⁸ C·m

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🔹 Q2

What happens to dipole in uniform electric field?

Answer:

It experiences torque but no net force, and aligns along the field direction.

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🔹 Q3

Compare field of dipole and point charge.

Answer:

Point charge field ∝ 1/r², dipole field ∝ 1/r³ → dipole field decreases faster.

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🔹 Q4

At what angle is torque maximum?

Solution:

τ = pE sinθ → maximum at sinθ = 1

θ = 90°

Answer: 90°

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🔹 Q5

When is potential energy minimum?

Solution:

U = −pE cosθ → minimum when cosθ = 1

Answer: θ = 0° (aligned with field)

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🔷 11. Advanced Conceptual Insight

Electric dipoles are fundamental in understanding polar molecules, dielectric behavior, and electromagnetic radiation. Oscillating dipoles produce electromagnetic waves, forming the basis of antennas and radiation theory.

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🔷 12. Applications

• Molecular polarity (H₂O, CO₂)
• Dielectric materials
• Capacitor design
• Radio wave transmission

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🔷 13. Summary

An electric dipole is a simple yet powerful system that explains many real-world electrostatic and electromagnetic phenomena. Its behavior in electric fields provides deep insights into molecular physics and modern technology.

✨ End of Chapter 10: Electric Dipole ✨