MIND GROW Magazine

Electrostatics – Stage 2 (Page 4)

Applications of Gauss’s Law

1️⃣ Electric Field due to Infinite Plane Sheet

Consider an infinite plane sheet with uniform surface charge density σ.

Choose a pill-box Gaussian surface crossing the sheet.

Field is perpendicular to sheet
Same magnitude on both sides

2EA = σA / ε₀

E = σ / (2ε₀)

⚠️ Important: Field is independent of distance from sheet.

2️⃣ Field due to Two Parallel Infinite Sheets

Same sign → fields cancel inside
Opposite sign → fields add inside

E = σ / ε₀ (between plates)

This is the basis of the parallel-plate capacitor.

3️⃣ Electric Field due to Charged Spherical Shell

(a) Outside the shell (r > R)

Gaussian surface: sphere of radius r.

E(4πr²) = Q / ε₀

E = 1/(4πε₀) · Q / r²

👉 Behaves like a point charge at center.

(b) Inside the shell (r < R)

Enclosed charge = 0

E = 0

⚠️ Very important IIT concept: Field inside hollow conductor is zero.

4️⃣ Electric Field due to Uniformly Charged Solid Sphere

(a) Outside the sphere (r > R)

Same as point charge:

E = 1/(4πε₀) · Q / r²

(b) Inside the sphere (r < R)

Enclosed charge:

Q_enc = Q · (r³

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