⚡ Electrostatics – Electric Charges & Fields

Page 4: Electric Dipole (Complete Concept for JEE)

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1. What is an Electric Dipole?

An electric dipole consists of two equal and opposite charges (+q and −q) separated by a small distance.

Examples:

• HCl molecule
• Water molecule (H₂O)
• Two charges +q and −q fixed at distance 2a

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2. Dipole Moment (Very Important)

Electric dipole moment is a vector quantity defined as:

p = q × 2a

• Direction: from −q to +q
• SI unit: Coulomb–meter (C·m)

JEE Note: Direction is always from negative to positive charge.

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3. Electric Field Due to Dipole (Axial Line)

Point lies on the line joining the two charges.

E_axial = (1 / 4πϵ₀) × (2p / r³)

• Field direction: same as dipole moment
• Strong field compared to equatorial line

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4. Electric Field Due to Dipole (Equatorial Line)

Point lies on the perpendicular bisector of dipole.

E_equatorial = (1 / 4πϵ₀) × (p / r³)

• Field direction: opposite to dipole moment
• Magnitude is half of axial field

Relation:

E_axial = 2 × E_equatorial

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5. Electric Field Due to Dipole (General Point)

Field depends on angle θ between dipole axis and position vector.

Result (Advanced Level):

E = (1 / 4πϵ₀) × (p / r³) √(1 + 3cos²θ)

Used mainly in JEE Advanced

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6. Electric Field Lines of a Dipole

• Start from +q and end at −q
• Symmetrical about dipole axis
• Do not intersect

Conceptual Questions frequently asked from this diagram.

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7. Torque on an Electric Dipole

When dipole is placed in a uniform electric field:

τ = pE sinθ

• Maximum torque at θ = 90°
• Zero torque at θ = 0° or 180°

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8. Stable and Unstable Equilibrium

• θ = 0° → Stable equilibrium
• θ = 180° → Unstable equilibrium

Very common JEE conceptual question.

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9. Potential Energy of Dipole

U = −pE cosθ

• Minimum energy at θ = 0°
• Maximum energy at θ = 180°

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10. Common JEE Traps & Mistakes

• Wrong direction of dipole moment
• Confusing axial and equatorial formulas
• Forgetting r³ dependence
• Mixing torque and force

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🎯 Page 4 Summary

• Dipole = two equal opposite charges
• p = q × 2a
• Axial field is twice equatorial field
• Torque aligns dipole with field
• Foundation for Gauss law & dielectrics