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Electromagnetic Induction question

2025 · 22 Jan · Shift 2 · Q58
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  5. /2025 · 22 Jan · Shift 2 · Q58

Electromagnetic Induction question

2025 · 22 Jan · Shift 2 · Q58

JEE MainPhysicsElectromagnetic InductionMCQ+4 / −1
A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnate field, the plot of magnitude of induced emf (ε)(\varepsilon)(ε) with time (t)(t)(t) is given by
  1. A
    JEE Main 2025 (Online) 22nd January Evening Shift Physics - Electromagnetic Induction Question 4 English Option 1
  2. B
    JEE Main 2025 (Online) 22nd January Evening Shift Physics - Electromagnetic Induction Question 4 English Option 2
  3. C
    JEE Main 2025 (Online) 22nd January Evening Shift Physics - Electromagnetic Induction Question 4 English Option 3
  4. D
    JEE Main 2025 (Online) 22nd January Evening Shift Physics - Electromagnetic Induction Question 4 English Option 4
View written solutionFree

Correct answer: B

  1. Use Faraday’s law

    The induced emf is

    ε=∣dΦBdt∣\varepsilon = \left|\frac{d\Phi_B}{dt}\right|ε=​dtdΦB​​​

    where magnetic flux through the loop is

    ΦB=BA\Phi_B = BAΦB​=BA

    as long as the part of the loop inside the magnetic field has area AAA.

  2. Loop moving out with constant speed

    Let the rectangular loop have side length ℓ\ellℓ perpendicular to the direction of motion, and let it move with constant speed vvv out of the uniform magnetic field region.

    While the loop is partially inside the field, the area inside the field decreases linearly with time:

    A(t)=ℓx(t)A(t) = \ell x(t)A(t)=ℓx(t)

    where x(t)x(t)x(t) is the length of the loop still inside the field.

    Since the loop moves with constant speed,

    x(t)=x0−vtx(t) = x_0 - vtx(t)=x0​−vt

    so

    A(t)=ℓ(x0−vt)A(t) = \ell(x_0-vt)A(t)=ℓ(x0​−vt)
  3. Flux variation

    Therefore,

    ΦB=Bℓ(x0−vt)\Phi_B = B\ell(x_0-vt)ΦB​=Bℓ(x0​−vt)

    Differentiating,

    dΦBdt=−Bℓv\frac{d\Phi_B}{dt} = -B\ell vdtdΦB​​=−Bℓv

    Hence the magnitude of induced emf is

    ε=Bℓv\varepsilon = B\ell vε=Bℓv

    which is constant while the loop is partially inside the magnetic field.

  4. Graph of ε\varepsilonε vs ttt

    So during the interval when the loop is leaving the field, the induced emf has a constant non-zero value.

    Before the loop starts leaving and after it completely leaves, flux does not change, so emf is zero. Thus the graph is a rectangular pulse: zero, then constant, then zero.

  5. Matching with options

    The option representing a constant magnitude of induced emf during the partial خروج interval is Option B.


Conclusion:

B\boxed{\text{B}}B​
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