Electrostatics – Stage 3
Electric Charges & Fields – Page 4
1. Electric Dipole – Core Definition
An electric dipole consists of two equal and opposite charges (+q, −q) separated by a small distance 2a.
Dipole Moment:
p = q × (2a)
Direction: from −q to +q
2. Field Due to Dipole – Axial Line
On the axial line of a dipole:
- Fields due to +q and −q act in same direction
- Magnitude is maximum
Result:
Eaxial = 2kp / r³
3. Field Due to Dipole – Equatorial Line
On the equatorial (perpendicular bisector) line:
- Horizontal components cancel
- Vertical components add
- Direction opposite to dipole moment
Result:
Eequatorial = kp / r³
4. JEE Trap – Direction Confusion
Most students remember magnitudes but forget directions.
Dangerous Trap:
On equatorial line, electric field is opposite to dipole moment.
5. Torque on Electric Dipole
When dipole is placed in uniform electric field:
- Net force = 0
- Torque tries to align dipole
Torque:
τ = pE sinθ
6. Stable & Unstable Equilibrium (PYQ Favorite)
| Orientation | Equilibrium |
|---|---|
| p ∥ E | Stable |
| p anti-parallel E | Unstable |
JEE Insight:
Minimum potential energy → stable equilibrium.
7. Potential Energy of Dipole
Potential energy of dipole in uniform field:
U = −pE cosθ
- U minimum when θ = 0°
- U maximum when θ = 180°
8. Non-Uniform Field – Hidden JEE Level
In non-uniform electric field:
- Net force ≠ 0
- Torque may also act
Advanced Trap:
Many assume zero force always — incorrect.
9. PYQ Thinking Pattern
- Ask: axial or equatorial?
- Check direction carefully
- Compare energy states
- Use symmetry before formula
Stage 3 – Page 4 Completed ✅
Next → Stage 3 – Page 5 (Electric Flux & Mixed Dipole Problems)
No comments:
Post a Comment