A rectangular wire loop of sides 6 cm and 3 cm has a small cut. It lies in a uniform magnetic field of 0.4 T normal to its plane, with its longer side along the edge of the field. The loop starts to move out of the field at a steady \(1.5\ \mathrm{cm\,s^{-1}}\), normal to its longer side. The emf across the cut lasts for
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2 s
An emf appears across the cut only while the flux through the loop changes. This happens while the loop is partly inside and partly outside the field. When the loop is wholly inside or wholly outside, the flux stays constant.
The loop moves normal to its longer side. So it is wholly out of the field after it moves a distance equal to its shorter side.
\( d=3\ \mathrm{cm} \)
\( v=1.5\ \mathrm{cm\,s^{-1}} \)
\( \begin{aligned} t &= \frac{d}{v} \\ &= \frac{3}{1.5} \\ &= 2\ \mathrm{s} \end{aligned} \)
The field of 0.4 T decides only the size of the emf.
NCERT (2026-27):
Example 6.4 – “Note that there are no induced current as long as the loops are completely inside or outside the region of the magnetic field.”