Electrostatics – Stage 3 (Page 9)

Capacitance, Energy Density & Electrostatic Pressure

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1️⃣ What is Capacitance (Real Meaning)

Capacitance is NOT about charge storage. It is about how easily a system allows electric field to exist.

Mathematically:

C = Q / V

But deeper meaning:

Capacitance depends ONLY on geometry + medium

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2️⃣ Field View of Capacitance (Very Important)

Electric field exists between conductors. Energy is stored in the FIELD, not on plates.

Capacitor = Field container

Parallel plate capacitor:

E = σ / ε₀ V = Ed C = ε₀A / d

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3️⃣ Energy Stored in a Capacitor

Three equivalent formulas:

• U = (1/2) C V²
• U = (1/2) Q V
• U = Q² / (2C)

Choose formula based on what is constant:

• Battery connected → V constant
• Isolated capacitor → Q constant

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4️⃣ Energy Density of Electric Field (IIT Favorite)

Energy stored per unit volume:

u = (1/2) ε₀ E²

Energy is everywhere the field exists

This idea is directly used in:

• Pressure on conductors
• Attraction between capacitor plates

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5️⃣ Electrostatic Pressure on Conductors

Charges repel each other. So conductor surface feels outward pressure.

P = (1/2) ε₀ E²

Same formula as energy density!

Interpretation:

Field stores energy → energy wants to expand → pressure acts.

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6️⃣ Force Between Capacitor Plates

Using pressure:

F = P × A = (1/2) ε₀ E² A

For parallel plate capacitor:

F = (1/2) ε₀ (V² / d²) A

Force exists even though plates attract each other

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7️⃣ Effect of Dielectric (Field Perspective)

Dielectric reduces electric field:

E = E₀ / K

Results:

• Capacitance increases
• Energy density decreases
• Force between plates reduces

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8️⃣ IIT-JEE Conceptual Traps

• Thinking energy is stored on plates ❌
• Forgetting battery condition (V constant vs Q constant)
• Confusing pressure direction

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9️⃣ Engineering Connection

• MEMS devices
• Electrostatic actuators
• Capacitor failure (plate bending)

All explained by:

Field energy + pressure

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🔟 Master Insight (Platinum)

Capacitance is geometry. Energy is in the field. Force comes from energy gradient.

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➡️ Next Page

Stage 3 – Page 10:
Mixed Advanced Problems (Capacitance + Field + Pressure) How IIT expects you to THINK