A small bar magnet is kept inside a closed cubical box. The magnetic flux through five faces of the box is \(+3\), \(-2\), \(+4\), \(-1\) and \(+1\), in units of \(10^{-4}\ \mathrm{Wb}\). Outward flux is taken as positive. The magnetic flux through the sixth face is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(-5\times10^{-4}\ \mathrm{Wb}\)
By Gauss’s law for magnetism, the net magnetic flux through any closed surface is zero. This holds even with a magnet inside the box, because a magnet has no isolated poles. Every field line that leaves the box enters it again somewhere else.
So the fluxes through the six faces must add up to zero.
\( \phi_1+\phi_2+\phi_3+\phi_4+\phi_5+\phi_6=0 \)
\( \begin{aligned} \phi_6 &= -(\phi_1+\phi_2+\phi_3+\phi_4+\phi_5) \\ &= -(3-2+4-1+1)\times10^{-4} \\ &= -5\times10^{-4}\ \mathrm{Wb} \end{aligned} \)
The negative sign shows that the flux through the sixth face is inward.
NCERT (2026-27):
Magnetism and Gauss’s Law – “Thus, Gauss’s law for magnetism is: The net magnetic flux through any closed surface is zero.”