The electric field due to an infinite plane sheet of charge with surface charge density σ is:
A. Zero
B. σ/ε₀
C. σ/(2ε₀)
D. 2σ/ε₀
Answer: Option C
Solution (By JKSSB Mock Tests)
Using Gauss's law, for an infinite sheet, electric field E = σ/(2ε₀), directed perpendicular to the sheet. This is uniform and independent of distance from the sheet. Option A is for field near conductor surface; C and D are incorrect. Memory aid: 'Infinite sheet: E = σ/(2ε₀); conductor surface: E = σ/ε₀'. This conceptual question tests electrostatics fundamentals, crucial for competitive exams. Always distinguish between conducting and non-conacting sheets, as field expressions differ due to charge distribution.
Explanation:
Equipotential surface has constant potential V everywhere. Work done W = qΔV; since ΔV = 0 along equipotential, W = 0. This holds for any path on the surface. Electric field is perpendicular to equipotential surfaces, so no work is done moving charge along them. Memory aid: 'Equipotential: ΔV=0 ⇒ W=0; field lines ⊥ equipotentials'. This electrostatics concept is frequently tested in competitive exams. Always link work to potential difference, not absolute potential; path independence is key for conservative fields.
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