Electrostatics – Stage 3 (Page 4)
Capacitor Networks & Dielectric Traps (IIT-JEE Advanced)
1️⃣ Why Capacitor Networks Are Dangerous
Capacitor problems look simple but hide deep traps.
Most wrong answers come from:
- Wrong identification of series / parallel
- Ignoring charge redistribution
- Forgetting dielectric effects
2️⃣ Fundamental Rules (Never Break These)
- Same charge → series
- Same potential → parallel
- Floating conductor → net charge conserved
✔ Draw nodes before equations
3️⃣ Capacitors with a Floating Conductor
A conductor not connected to battery:
- Total charge on conductor = constant
- Charges redistribute internally
✔ This is NOT series or parallel directly
Solve using:
- Charge conservation
- Potential continuity
4️⃣ Dielectric Slab Inserted Partially
When dielectric is inserted:
- Capacitance increases
- Electric field inside reduces
⚠️ Partial insertion creates non-uniform field
Treat system as:
- Two capacitors in parallel (area split)
5️⃣ Force on Dielectric Slab (Classic IIT Question)
Dielectric always moves toward:
Region of higher electric field
Reason:
- System tries to minimize energy
✔ Use energy method, not force formula
6️⃣ Capacitor with Battery Connected vs Disconnected
| Condition | Battery Connected | Battery Disconnected |
|---|---|---|
| Voltage | Constant | Changes |
| Charge | Changes | Constant |
| Energy | May increase or decrease | Always decreases |
7️⃣ Superposition Trap in Capacitor Networks
Voltage is NOT conserved — Charge is local
Common mistake:
- Adding voltages blindly
Correct approach:
- Apply superposition node-wise
- Calculate charge separately
8️⃣ Equivalent Capacitance Is NOT Enough
IIT rarely asks only Ceq.
They ask:
- Individual capacitor charge
- Energy stored in each
- Potential difference between internal nodes
✔ Always solve full network
9️⃣ Energy Stored – Hidden Comparison Trick
Energy stored:
U = ½ C V² = Q² / (2C)
Which formula to use?
- Use V-form if battery connected
- Use Q-form if isolated
🔟 Final IIT Survival Checklist
✔ Identify nodes first ✔ Check battery connection ✔ Conserve charge on isolated conductors ✔ Use energy for force problems ✔ Never assume symmetry blindly
➡️ Next Page
Stage 3 – Page 5:
Electrostatic Energy, Work Done & Field–Energy Relations (Advanced Level)
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