Electrostatics – Stage 3

Electric Charges & Fields – Page 6

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1. Infinite Line Charge

Consider an infinitely long straight wire with uniform linear charge density λ (C/m).

Gaussian Surface:
Cylindrical surface coaxial with the wire

By symmetry:

• E is radial
• E is constant on curved surface
• No flux through flat ends

Result:
E = λ / (2π ε₀ r)

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2. Infinite Plane Sheet of Charge

Consider an infinite plane with surface charge density σ (C/m²).

Gaussian Surface:
Thin pillbox crossing the sheet

• Field is perpendicular to sheet
• Same magnitude on both sides

Electric Field:
E = σ / (2 ε₀)

Important: Field is independent of distance.

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3. Conducting Infinite Sheet

• Electric field inside conductor = 0
• Entire charge resides on surface

E (outside) = σ / ε₀

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4. Spherical Charge Distribution (Point Charge)

For a point charge q at center of spherical Gaussian surface:

E = 1 / (4π ε₀) · q / r²

• Same as Coulomb’s law
• Gauss law gives quick derivation

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5. Uniformly Charged Solid Sphere

Total charge Q, radius R.

Outside Sphere (r ≥ R)

E = 1 / (4π ε₀) · Q / r²

Inside Sphere (r < R)

E = 1 / (4π ε₀) · (Q r / R³)

• E ∝ r inside
• Maximum at surface

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6. Conducting Sphere

• All charge on surface
• E inside conductor = 0
• Outside behaves like point charge

JEE Trap:
Solid sphere ≠ Conducting sphere

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7. Field vs Distance – Comparison Table

System	E vs r
Line charge	E ∝ 1/r
Plane sheet	E = constant
Point charge	E ∝ 1/r²
Solid sphere (inside)	E ∝ r

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8. JEE Advanced Problem Strategy

• Check symmetry before using Gauss law
• Choose Gaussian surface carefully
• Never assume Gauss law always simplifies

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Stage 3 – Page 6 Completed ✅

Next → Stage 3 – Page 7 (Electric Field due to Charged Ring, Disc & Shell)