Electrostatics – Stage 3

Electric Charges & Fields – Page 8

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1. Electric Dipole – Basic Definition

An electric dipole consists of two equal and opposite charges (+q and −q) separated by a small distance 2a.

Dipole Moment (p):
p = q × 2a
Direction: from −q to +q

• Vector quantity
• Unit: Coulomb-meter (C·m)

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2. Electric Field due to Dipole – Axial Line

Point lies on the axis of the dipole at distance r from center (r ≫ a).

Electric Field (Axial):
E_axial = (1 / 4π ε₀) · (2p / r³)

• Direction: along dipole moment
• Falls faster than point charge (∝ 1/r³)

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3. Electric Field due to Dipole – Equatorial Line

Point lies on perpendicular bisector of dipole.

Electric Field (Equatorial):
E_eq = (1 / 4π ε₀) · (p / r³)

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

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4. Torque on a Dipole in Uniform Electric Field

When dipole is placed in uniform electric field E at angle θ.

Torque:
τ = p E sinθ

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

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5. Stable and Unstable Equilibrium

Orientation	θ	Nature
Parallel to field	0°	Stable
Anti-parallel to field	180°	Unstable

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6. Potential Energy of Dipole in Electric Field

Potential Energy:
U = −p E cosθ

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

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7. JEE Advanced Thinking & Traps

• Never confuse axial and equatorial formulas
• Remember: both fields vary as 1/r³
• Torque exists only in uniform field
• Force on dipole exists only in non-uniform field

Common JEE Trap:
Using point charge field (1/r²) for dipole problems ❌

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Stage 3 – Page 8 Completed ✅

Next → Stage 3 – Page 9 (Dipole in Non-uniform Field & Applications)