A small flat surface is placed in a uniform electric field. The electric flux through the surface is zero when
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → the plane of the surface is parallel to the field
The flux through a small flat area is \( \Delta\phi=E\,\Delta S\cos\theta \). Here \( \theta \) is the angle between the field and the normal to the area.
Option (1) the plane of the surface is parallel to the field — Correct. The normal to the surface is then at \( 90^\circ \) to the field, so \( \cos\theta=0 \). The field lines run along the surface and do not cross it.
Option (2) the surface is moved to another point in the field without turning it — Incorrect. In a uniform field, \( E \) is the same at every point. The angle \( \theta \) does not change either, so the flux stays the same and does not become zero.
Option (3) the normal to the surface makes an angle of \( 45^\circ \) with the field — Incorrect. The flux is \( E\,\Delta S\cos45^\circ \), about \( 0.71\,E\,\Delta S \). It is smaller than the largest value but not zero.
Option (4) the direction of the field is reversed — Incorrect. Reversing the field changes \( \theta \) to \( 180^\circ-\theta \). The flux changes sign but keeps its size.
NCERT (2026-27):
Electric Flux – “… Thus, the number of field lines crossing ΔS is proportional to E ΔS cosθ. When θ = 90°, field lines will be parallel to ΔS and will not cross it at all ….”
Electric Flux – “… Electric flux Δφ through an area element ΔS is defined by Δφ = E.ΔS = E ΔS cosθ … The angle θ here is the angle between E and ΔS.”