MIND GROW Magazine

Electrostatics – Stage 3 (Page 2)

Force on Dielectric & Variable Capacitors (JEE Advanced Core)

1️⃣ Why JEE Loves Dielectric Problems

Dielectric problems test thinking, not formulas.

Most students try:

Coulomb force ❌
Direct force formulas ❌

But IIT expects:

Energy method ✔
Field reasoning ✔

2️⃣ Fundamental Rule (Golden Rule)

Force = − dU / dx

Where:

U = energy of system
x = position of slab / plate

This single rule solves 90% JEE capacitor force problems.

3️⃣ Dielectric Slab Entering Capacitor

Consider:

Parallel plate capacitor
Dielectric slab partially inside
Battery disconnected

Key idea: Capacitance increases as slab enters.

4️⃣ Battery Disconnected Case

Conditions:

Charge Q = constant
Capacitance C increases

Energy formula:

U = Q² / (2C)

As C increases → U decreases

✔ System tries to minimize energy ✔ Slab is pulled inside automatically

5️⃣ Battery Connected Case

Conditions:

Voltage V = constant
Capacitance C increases

Energy formula:

U = ½ C V²

As C increases → U increases

⚠️ Extra energy supplied by battery ⚠️ Still slab is pulled inside

6️⃣ Why Slab Always Moves Inside?

Because system + battery energy is minimized.

Field prefers:

Lower field region
Higher permittivity medium

This is pure field logic.

7️⃣ Variable Plate Separation (Moving Plate)

Consider:

One plate movable
Other fixed

Capacitance:

C = ε₀ A / d

As distance d changes → energy changes.

8️⃣ Force Between Capacitor Plates

Using energy method:

F = − dU / dd

Final result:

F = ½ ε₀ A E²

✔ Same as field pressure result ✔ Confirms energy–field consistency

9️⃣ JEE Advanced Trap

⚠️ Students forget to check:

Battery connected or not
What is changing (x or d)
What is constant (Q or V)

Always identify constraints first.

🔟 What You Must Remember

✔ Force = − dU/dx ✔ Dielectric always pulled inside ✔ Battery ON/OFF logic critical ✔ Field energy explains motion ✔ No Coulomb force needed

➡️ Next Page

Stage 3 – Page 3:
Capacitors in Non-Uniform Fields + Edge Effects + JEE Traps

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