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Electromagnetic Induction question

2009 · Shift 1 · Q43
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Electromagnetic Induction question

2009 · Shift 1 · Q43

JEE AdvancedPhysicsElectromagnetic InductionMCQ+3 / −1
The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. I1I_1I1​ and I2I_2I2​ are the currents in the segments ab and cd. Then, IIT-JEE 2009 Paper 1 Offline Physics - Electromagnetic Induction Question 6 English
  1. A
    I1>I2I_1 \gt I_2I1​>I2​
  2. B
    I1<I2I_1 \lt I_2I1​<I2​
  3. C
    I1I_1I1​ is in the direction ba and I2I_2I2​ is in the direction cd.
  4. D
    I1I_1I1​ is in the direction ab and I2I_2I2​ is in the direction dc.
View written solutionFree

Correct answer: D

  1. Use Lenz’s law to find the sense of induced current

    The magnetic field is into the plane and its magnitude is increasing with time.

    By Lenz’s law, the induced current must oppose this increase, so it must produce a magnetic field out of the plane.

    A current that produces magnetic field out of the plane is anticlockwise.

    Therefore, in the loop:

    • on the left vertical branch, current flows upward,
    • on the right vertical branch, current flows downward.

    Hence,

    • in segment ababab, current is in the direction ababab,
    • in segment cdcdcd, current is in the direction dcdcdc.

    So the directional statement in Option D is correct, while Option C is incorrect.

  2. Compare magnitudes I1I_1I1​ and I2I_2I2​

    Since the arrangement is one closed conducting loop, the induced current circulates around the loop. In a series loop, the same current passes through all segments.

    Therefore, the magnitudes of current in segments ababab and cdcdcd are equal: I1=I2.I_1 = I_2.I1​=I2​.

    So:

    • Option A (I1>I2I_1 > I_2I1​>I2​) is false,
    • Option B (I1<I2I_1 < I_2I1​<I2​) is false.
  3. Final answer

    The only correct option is: D\boxed{D}D​

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