Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): A small flat area is first held normal to a uniform electric field. When it is turned so that its normal makes an angle of \(60^\circ\) with the field, the electric flux through it becomes half.
Reason (R): The electric flux through an area element \(\Delta S\) is \(E\,\Delta S\cos\theta\), where \(\theta\) is the angle between \(\vec E\) and the normal to the area element.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Both (A) and (R) are correct and (R) is the correct explanation of (A).
Assertion (A) A small flat area is first held normal to a uniform electric field. When it is turned so that its normal makes an angle of \(60^\circ\) with the field, the electric flux through it becomes half. — True. At first \( \theta=0^\circ \) and the flux is \( E\,\Delta S \). After turning, \( \theta=60^\circ \) and \( \cos60^\circ=\frac{1}{2} \), so the flux is \( \frac{1}{2}E\,\Delta S \).
Reason (R) The electric flux through an area element \(\Delta S\) is \(E\,\Delta S\cos\theta\), where \(\theta\) is the angle between \(\vec E\) and the normal to the area element. — True. This is the definition of electric flux. Only the projection \( \Delta S\cos\theta \) of the area normal to the field counts.
Why Reason (R) explains Assertion (A)?
The flux depends on the angle through the factor \( \cos\theta \).
Turning the area from \( 0^\circ \) to \( 60^\circ \) changes this factor from 1 to \( \frac{1}{2} \). So the flux becomes half, as the Assertion says.
NCERT (2026-27):
Electric Flux – “… The projection of the area element normal to E is ΔS cosθ. Thus, the number of field lines crossing ΔS is proportional to E ΔS cosθ.”
Electric Flux – “We now come to the definition of electric flux. Electric flux Δφ through an area element ΔS is defined by Δφ = E.ΔS = E ΔS cosθ …”