In an electric field, a small flat area is held normal to the field lines, first at a point P and then at a point Q. Twelve field lines cross this area at P, and three field lines cross the same area at Q. The electric field at P is \(400\ \mathrm{N\,C^{-1}}\). The electric field at Q is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(100\ \mathrm{N\,C^{-1}}\)
The number of field lines crossing a small area held normal to the field is proportional to \( E\,\Delta S \). Here the area is the same at both points. So the field is proportional to the number of lines crossing it.
\( \begin{aligned} E_Q &= E_P\times\frac{N_Q}{N_P} \\ &= 400\times\frac{3}{12} \\ &= 100\ \mathrm{N\,C^{-1}} \end{aligned} \)
Fewer lines cross the area at Q, so the field there is weaker.
NCERT (2026-27):
Electric Flux – “In the picture of electric field lines described above, we saw that the number of field lines crossing a unit area, placed normal to the field at a point is a measure of the strength of electric field at that point.”