Given below are two statements:
Statement I: For a single point charge, the number of field lines crossing a sphere centred on the charge does not depend on the radius of the sphere.
Statement II: Electrostatic field lines do not form closed loops, because the electrostatic field is conservative.
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 Statement I and Statement II are correct
Field lines show the direction of the field. How closely they are packed shows its strength.
Statement I For a single point charge, the number of field lines crossing a sphere centred on the charge does not depend on the radius of the sphere. — True. The field of a point charge falls as \( 1/r^{2} \), while the area of a sphere around it grows as \( r^{2} \). The two changes balance, so the same number of lines crosses every such sphere.
Statement II Electrostatic field lines do not form closed loops, because the electrostatic field is conservative. — True. A field line starts on a positive charge and ends on a negative charge. Because the electrostatic field is conservative, a line can never come back to close on itself.
NCERT (2026-27):
Electric Field Lines – “… Since the electric field decreases as the square of the distance from a point charge and the area enclosing the charge increases as the square of the distance, the number of field lines crossing the enclosing area remains constant, whatever may be the distance of the area from the charge.”
Electric Field Lines – “(iv) Electrostatic field lines do not form any closed loops. This follows from the conservative nature of electric field …”