Electrostatics – Stage 3 (Page 1)
Electric Field Energy + Gauss Law Thinking
1️⃣ Shift of Mindset (Very Important)
Stage 1 & 2 → Charges & Voltages Stage 3 → Fields store energy
In advanced electrostatics, we stop asking:
- How much charge?
- What voltage?
We start asking:
- Where is energy stored?
- How does field distribute?
2️⃣ Energy Stored in Electric Field
Energy is NOT stored on plates. Energy is stored in the electric field between them.
Energy density (u) = ½ ε₀ E²
👉 This formula connects Gauss Law + Capacitors + Energy.
3️⃣ From Capacitor Formula to Field Formula
We already know:
U = ½ C V²
Using:
- C = ε₀A / d
- E = V / d
We get:
U = ½ ε₀ E² (A d)
✔ Energy = energy density × volume
4️⃣ Gauss Law – Field Creator
∮ E · dA = Qinside / ε₀
Gauss law answers:
- What is E at a point?
- How field changes in space?
⚠️ Gauss law works BEST with symmetry.
5️⃣ Parallel Plate Capacitor via Gauss Law
For infinite plates:
- Uniform field
- No fringing
E = σ / ε₀
Using V = Ed:
C = ε₀ A / d
🔥 Capacitor formula comes directly from Gauss Law.
6️⃣ Dielectric – Field Perspective
When dielectric is inserted:
- Field reduces
- Capacitance increases
E = E₀ / K
C = K C₀
⚠️ Field changes, not charge (if battery disconnected).
7️⃣ Energy with Dielectric (JEE Favourite)
Battery disconnected:
- Charge constant
- Energy decreases
Battery connected:
- Voltage constant
- Energy increases
⚠️ Always check: battery ON or OFF.
8️⃣ Field Pressure on Plates
Electric field exerts pressure:
Pressure = ½ ε₀ E²
This explains:
- Attraction between plates
- Force in variable capacitors
9️⃣ Advanced JEE Insight
Force on capacitor plate = Rate of change of field energy
Mechanical + Electrical energy are linked.
🔟 What You Should Master from This Page
✔ Energy density concept ✔ Gauss law → capacitor derivation ✔ Dielectric field behavior ✔ Battery ON/OFF logic ✔ Field-based force thinking
➡️ Next Page
Stage 3 – Page 2:
Force on Dielectric Slab + Variable Capacitors (Top 5 JEE Problems)
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