Electrostatics – Stage 3

Electric Charges & Fields – Page 9

                                                  

---

1. Uniform vs Non-Uniform Electric Field

Uniform Field	Non-Uniform Field
Electric field same everywhere	Electric field changes with position
No net force on dipole	Net force acts on dipole
Only torque acts	Torque + force both act

---

2. Force on Electric Dipole in Non-Uniform Field

In a non-uniform electric field, forces on +q and −q are unequal. Hence, a net force acts on the dipole.

Key Result:
Force on dipole ∝ gradient of electric field

For a dipole aligned with field:

Approximate Expression:
F ≈ p · (dE / dx)

• Dipole moves toward stronger field region
• Basis of dielectrophoresis

---

3. Motion of Dipole in Electric Field

A dipole in electric field can show:

• Rotational motion (due to torque)
• Translational motion (due to force)

Important:
In uniform field → only rotation
In non-uniform field → rotation + translation

---

4. Small Oscillations of Dipole (Advanced)

Dipole placed in uniform electric field and slightly displaced from stable equilibrium.

Angular Frequency:
ω = √(pE / I)

• I = moment of inertia of dipole
• Motion is simple harmonic (SHM)

---

5. Work Done in Rotating Dipole

Work done in rotating dipole from θ₁ to θ₂:

Work Done:
W = pE (cosθ₁ − cosθ₂)

• Depends only on initial and final positions
• Independent of path

---

6. Dipole in Gravitational Analogy (JEE Insight)

• Electric dipole ↔ magnetic dipole
• pE ↔ mB
• Torque τ = pE sinθ ↔ τ = mB sinθ

JEE Trick:
Many electrostatics problems can be solved using magnetic dipole analogy

---

7. JEE Advanced Traps & Mistakes

• Assuming force exists in uniform field ❌
• Forgetting direction of force toward stronger field
• Confusing torque and force expressions
• Ignoring rotational motion in combined problems

---

Stage 3 – Page 9 Completed ✅

Next → Stage 3 – Page 10 (Gauss Law – Conceptual & Mathematical Foundation)