A region in the form of an equilateral triangle (in x-y plane) of height L has a uniform magnetic field B pointing in the +z-direction. A conducting loop PQR, in the form of an equilateral triangle of the same height L, is placed in the x−y plane with its vertex P at x=0 in the orientation shown in the figure. At t=0, the loop starts entering the region of the magnetic field with a uniform velocity v along the +x-direction. The plane of the loop and its orientation remain unchanged throughout its motion.
Which of the following graph best depicts the variation of the induced emf(E) in the loop as a function of the distance (x) starting from x=0?
(A)(see structure)✓ Correct
(B)(see structure)
(C)(see structure)
(D)(see structure)
Answer: (A)
Solution
As the loop enters the magnetic field region from x=0 to x=L, the effective length cutting the field increases linearly with x. The induced emf is ε=Bℓeffv=B×3xv, which is linear in x.
From x=L to x=2L, both the loop and field region overlap partially. The net flux change involves both entry and exit effects. The emf becomes ∣emf∣=3Bv[4L−3x], which is linear but decreasing. At x=34L, the emf becomes zero.
Option (A) correctly shows this behavior: linear increase from 0 to L, then linear decrease crossing zero at x=34L, continuing to x=2L.
JEE Advanced · 2024 · 26 May 2024 · Paper 2 · Single correct option
