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Electromagnetic Induction question

2020 · 7 Jan · Shift 1 · Q61
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  5. /2020 · 7 Jan · Shift 1 · Q61

Electromagnetic Induction question

2020 · 7 Jan · Shift 1 · Q61

JEE MainPhysicsElectromagnetic InductionMCQ+4 / −1
Consider a circular coil of wire carrying constant current I, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by ϕ\phiϕ i. The magnetic flux through the area of the circular coil area is given by ϕ\phiϕ 0. Which of the following option is correct?
  1. A
    ϕ\phiϕ i = ϕ\phiϕ 0
  2. B
    ϕ\phiϕ i < ϕ\phiϕ 0
  3. C
    ϕ\phiϕ i >ϕ\gt \phi>ϕ 0
  4. D
    ϕ\phiϕ i = - ϕ\phiϕ 0
View written solutionFree

Correct answer: D

  1. Key idea: use Gauss's law for magnetism
    For any magnetic field, ∮B⃗⋅dA⃗=0\oint \vec B \cdot d\vec A = 0∮B⋅dA=0 because magnetic monopoles do not exist.

  2. Construct a closed surface
    Take the given infinite plane containing the circular coil. The coil divides the plane into:

    • the interior circular area of the loop,
    • the remaining infinite plane area outside the loop.

    Imagine this plane as a boundary of a very thin closed surface (a pillbox-like surface) with one face just above the plane and one face just below it.

  3. Flux through the closed surface
    Since the magnetic field is continuous and the side area can be made negligible, the total magnetic flux through the entire plane must satisfy: ϕ0+ϕi=0\phi_0 + \phi_i = 0ϕ0​+ϕi​=0 where

    • ϕ0\phi_0ϕ0​ = flux through the circular area,
    • ϕi\phi_iϕi​ = flux through the rest of the infinite plane.

  4. Relation between the two fluxes
    Therefore, ϕi=−ϕ0\phi_i = -\phi_0ϕi​=−ϕ0​

  5. Check options

    • A: ϕi=ϕ0\phi_i=\phi_0ϕi​=ϕ0​ ❌
    • B: ϕi<ϕ0\phi_i<\phi_0ϕi​<ϕ0​ ❌ (not the exact general relation)
    • C: ϕi>ϕ0\phi_i>\phi_0ϕi​>ϕ0​ ❌
    • D: ϕi=−ϕ0\phi_i=-\phi_0ϕi​=−ϕ0​ ✅

Thus the correct option is D.

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