Which statement correctly describes the electric field due to an infinite plane sheet of charge with surface density σ?

Which statement correctly describes the electric field due to an infinite plane sheet of charge with surface density σ?

• A. The field is parallel to the sheet
• B. The field is perpendicular to the sheet with magnitude ε0/σ on each side
• C. The field is zero on both sides
• D. The field is perpendicular to the sheet with magnitude σ/(2 ε0) on each side

Answer: (D)

An infinite plane of charge creates a uniform electric field that is perpendicular to the plane on both sides, and its strength does not depend on distance from the plane. Using Gauss’s law with a pillbox straddling the plane, the enclosed charge is σA and the total outward flux is E A on each side, so 2E A = σA/ε0, giving E = σ/(2ε0). The field points away from the plane for positive σ (toward it for negative σ). So the description that fits is a field perpendicular to the sheet with magnitude σ/(2ε0) on each side. The field is not parallel to the sheet, the magnitude isn’t ε0/σ, and the field is not zero.

An infinite plane of charge creates a uniform electric field that is perpendicular to the plane on both sides, and its strength does not depend on distance from the plane. Using Gauss’s law with a pillbox straddling the plane, the enclosed charge is σA and the total outward flux is E A on each side, so 2E A = σA/ε0, giving E = σ/(2ε0). The field points away from the plane for positive σ (toward it for negative σ).

So the description that fits is a field perpendicular to the sheet with magnitude σ/(2ε0) on each side. The field is not parallel to the sheet, the magnitude isn’t ε0/σ, and the field is not zero.