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Electromagnetic Induction · Question 3

JEE Advanced 2025 Paper 1MCQHard📈 Topic in 33% papers+4−1
1

A conducting square loop initially lies in the XZ plane with its lower edge hinged along the X-axis. Only in the region y 0, there is a time dependent magnetic field pointing along the Z-direction, B(t)=B0( t) k, where B0 is a constant. The magnetic field is zero everywhere else. At time t=0, the loop starts rotating with constant angular speed about the X axis in the clockwise direction as viewed from the +X axis (as shown in the figure). Ignoring self-inductance of the loop and gravity, which of the following plots correctly represents the induced e.m.f. (V) in the loop as a function of time: [figure]

  1. [figure]
  2. [figure]
  3. [figure]
  4. [figure]

Answer

(1) [figure]

Solution

At time t the loop (side L) makes angle t with the Z-axis; its projection on the XY plane has area L2 t, lying in y 0 for 0< t< .

For 0<t< : =B0 t L2 t= B0L22 2 t

V=- d dt=-B0L2 2 t: starts at -B0L2 , rises to +B0L2 at t= 2 , back to -B0L2 at t= .

For <t< 2 the loop is in y<0 where B=0: =0, V=0 (sudden drop to zero at ).

From 2 the pattern repeats — this is plot (A).

Answer: (A)

JEE Advanced 2025 Paper 1

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2

A conducting square loop of side L, mass M and resistance R is moving in the XY plane with its edges parallel to the X and Y axes. The region y 0 has a uniform magnetic field, B=B0 k. The magnetic field is zero everywhere else. At time t=0, the loop starts to enter the magnetic field with an initial velocity v0 j m/s, as shown in the figure. Considering the quantity K= B02L2RM in appropriate units, ignoring self-inductance of the loop and gravity, which of the following statements is/are correct: [figure]

  1. If v0=1.5KL, the loop will stop before it enters completely inside the region of magnetic field.
  2. When the complete loop is inside the region of magnetic field, the net force acting on the loop is zero.
  3. If v0= KL10, the loop comes to rest at t= ( 1K ) ( 52 ).
  4. If v0=3KL, the complete loop enters inside the region of magnetic field at time t= ( 1K ) ( 32 ).
JEE Advanced 2025 Paper 1
3

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. [figure] 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?

  1. [figure]
  2. [figure]
  3. [figure]
  4. [figure]
JEE Advanced 2024 Paper 2

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