Q.Consider an infinite thin plane lamina of uniformly positive charged having a surface charge density σ. At a point P of distance r very near to the lamina, electric field intensity is E. How does the electric field vary with distance ?

An infinite uniformly charged plane produces a uniform field E = σ/2ε₀ that does not depend on distance from the sheet, so the E–r graph is a horizontal straight line. Option (d).

Step 1 — apply Gauss's law with a cylindrical (pillbox) surface piercing the sheet, a standard NCERT/CBSE Class 12 Physics derivation. The field emerges perpendicular to the sheet from both faces.

Step 2 — the result is E = σ/(2ε₀), with no r in the expression.

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Between two oppositely-charged parallel sheets, the fields of both sheets point the same way and add: $E=\sigma/\varepsilon_0$.

Each infinite charged sheet of surface density $\sigma$ produces a field of magnitude $\sigma/2\varepsilon_0$ on either side, directed away from a positive sheet and toward a negative sheet.

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