The figure shows the field lines of (a) a bar magnet, (b) a current-carrying finite solenoid and (c) an electric dipole. The curves marked i and ii are closed surfaces.
Which of the following is correct about the net flux of the field through the closed surface ii?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → It is zero in (a) and (b), and outward in (c).
Magnetic field lines are continuous and form closed loops. So as many magnetic lines leave a closed surface as enter it, and the net magnetic flux is zero. Electric field lines start on a positive charge and end on a negative charge. So a closed surface that holds a net charge has a net flux through it.
Option (1) It is zero in all three cases. — Incorrect. In (c), the surface ii holds the positive charge of the dipole. More lines leave this surface than enter it.
Option (2) It is outward in (a) and (b), and zero in (c). — Incorrect. In (a) and (b), the lines that leave surface ii outside the magnet are the same lines that enter it from inside. Their flux balances to zero. In (c) the surface holds a net charge, so the flux is not zero.
Option (3) It is outward in (a), and zero in (b) and (c). — Incorrect. A bar magnet and a solenoid have the same kind of closed field lines. So the flux through ii is zero in (a), just as in (b). In (c) it is not zero.
Option (4) It is zero in (a) and (b), and outward in (c). — Correct. The magnetic lines through ii balance in (a) and (b). In (c) the surface ii holds a net positive charge, so there is a net outward flux.
NCERT (2026-27):
Magnetism and Gauss’s Law – “… In Fig 5.2(c), we see that for a closed surface represented by i , the number of lines leaving the surface is equal to the number of lines entering it. … However, in the same figure, for the closed surface ii , there is a net outward flux, since it does include a net (positive) charge.”
Magnetism and Gauss’s Law – “The situation is radically different for magnetic fields which are continuous and form closed loops. Examine the Gaussian surfaces represented by i or ii in Fig 5.2(a) or Fig. 5.2(b). Both cases visually demonstrate that the number of magnetic field lines leaving the surface is balanced by the number of lines entering it. The net magnetic flux is zero for both the surfaces.”
FIGURE 5.2 The field lines of (a) a bar magnet, (b) a current-carrying finite solenoid and (c) electric dipole. At large distances, the field lines are very similar. The curves labelled i and ii are closed Gaussian surfaces.