⚡ Electrostatics – Electric Charges & Fields
Page 10: Electric Dipole – Field, Torque, Energy (JEE Advanced Level)
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1. What is an Electric Dipole?
An electric dipole consists of two equal and opposite charges separated by a small distance.
Dipole moment:
p = q × 2a
- Direction: from negative to positive charge
- Vector quantity
- Unit: Coulomb–meter (C·m)
2. Electric Field due to Dipole (Axial Line)
Axial line is the line joining the two charges.
Electric field on axial line:
Eaxial = (1 / 4πϵ₀) × (2p / r³)
- Direction: same as dipole moment
- Falls as 1/r³ (faster than point charge)
3. Electric Field due to Dipole (Equatorial Line)
Equatorial line is the perpendicular bisector of dipole.
Electric field on equatorial line:
Eequatorial = (1 / 4πϵ₀) × (p / r³)
- Direction: opposite to dipole moment
- Half of axial field magnitude
4. Comparison Table (Very Important)
| Property | Axial Line | Equatorial Line |
|---|---|---|
| Magnitude | 2kp/r³ | kp/r³ |
| Direction | Along p | Opposite to p |
5. Torque on Electric Dipole in Uniform Field
When a dipole is placed in a uniform electric field, it experiences torque.
τ = pE sinθ
- Maximum torque at θ = 90°
- Zero torque at θ = 0° and 180°
- Torque tries to align dipole with field
6. Potential Energy of Electric Dipole
U = −pE cosθ
- Minimum energy at θ = 0° (stable)
- Maximum energy at θ = 180° (unstable)
- Dipole naturally aligns with field
7. Stable vs Unstable Equilibrium
- θ = 0° → Stable equilibrium
- θ = 180° → Unstable equilibrium
- Small displacement decides behavior
8. JEE Advanced Conceptual Traps
- Dipole in uniform field → No net force
- Non-uniform field → Net force exists
- Field decreases as 1/r³, not 1/r²
- Torque ≠ force
9. Conceptual Question (JEE Level)
Question:
Can an electric dipole have zero net force but non-zero torque?
Answer:
- Uniform electric field → Zero force
- Dipole tilted → Torque present
10. Final Exam Tips
- Memorize axial & equatorial formulas
- Always note direction of field
- Use symmetry wherever possible
- Draw rough sketch before solving
🎯 Page 10 Summary
- Dipole moment is the heart of dipole physics
- Torque aligns dipole with field
- High weightage in JEE Advanced
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