Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Electromagnetic Induction question

2012 · Shift 2 · Q60
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Advanced
  3. /Physics
  4. /Electromagnetic Induction
  5. /2012 · Shift 2 · Q60

Electromagnetic Induction question

2012 · Shift 2 · Q60

JEE AdvancedPhysicsElectromagnetic InductionMultiple correct+4 / −2
A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it, the correct statement(s) is(are)
  1. A
    the emf induced in the loop is zero if the current is constant.
  2. B
    the emf induced in the loop is finite if the current is constant.
  3. C
    the emf induced in the loop is zero if the current decreases at a steady state
  4. D
    the emf induced in the loop is finite if the current decreases at a steady state.
View written solutionFree

Correct answer: A, C

  1. Set up the geometry

A circular loop lies in a plane, and an infinitely long straight wire is placed along a diameter of the loop, in the same plane, without touching it.

Let the loop be in the plane of the page. The magnetic field due to the long straight wire is perpendicular to the plane of the loop:

  • on one side of the wire, it is into the page,
  • on the other side, it is out of the page.

So the loop is divided into two equal halves by the wire, and the magnetic flux through these two halves has equal magnitude but opposite sign.

  1. Magnetic field due to the straight wire

At a perpendicular distance rrr from a long straight wire carrying current III,

B=μ0I2πr.B = \frac{\mu_0 I}{2\pi r}.B=2πrμ0​I​.

The direction of B⃗\vec BB changes on the two sides of the wire.

  1. Net magnetic flux through the loop

The magnetic flux through the loop is

Φ=∫B⃗⋅dA⃗.\Phi = \int \vec B \cdot d\vec A.Φ=∫B⋅dA.

Because the wire lies along a diameter:

  • every area element on one semicircle has a corresponding area element on the other semicircle at the same distance from the wire,
  • the magnitudes of BBB at these corresponding points are equal,
  • but their directions relative to the chosen area vector are opposite.

Hence, the flux through one semicircle cancels the flux through the other semicircle.

Therefore,

Φ=0\Phi = 0Φ=0

at all times (for any value of current III, as long as the wire remains along the diameter).

  1. Induced emf

By Faraday’s law,

E=−dΦdt.\mathcal{E} = -\frac{d\Phi}{dt}.E=−dtdΦ​.

Since the net flux is always zero, we get

E=−d(0)dt=0.\mathcal{E} = -\frac{d(0)}{dt} = 0.E=−dtd(0)​=0.

This remains true whether:

  • the current is constant, or
  • the current decreases uniformly with time.

Even though the magnetic field at each point may change when current changes, the total flux through the loop remains identically zero because of symmetry.

  1. Evaluate the options

  • A: the emf induced in the loop is zero if the current is constant.
    Correct.

  • B: the emf induced in the loop is finite if the current is constant.
    Incorrect.

  • C: the emf induced in the loop is zero if the current decreases at a steady state.
    Correct.

  • D: the emf induced in the loop is finite if the current decreases at a steady state.
    Incorrect.

  1. Final answer

The correct options are

A, C\boxed{A,\ C}A, C​
PreviousNext

More from Electromagnetic Induction

  • 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. I1​… Includes diagram2009 · MCQ
  • Two metallic rings A and B, identical in shape and size but having different resistivities ρA​ and ρB​, are kept on top of two identical solenoids as shown in the figure below. When current I is switched on in both the solenoids… Includes diagram2009 · Multiple correct
  • 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​(cosωt)k^… Includes diagram2025 · MCQ
  • 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… Includes diagram2025 · Multiple correct
  • 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… Includes diagram2024 · MCQ
  • A thin conducting rod MN of mass 20 gm, length 25 cm and resistance 10 Ω is held on frictionless, long, perfectly conducting vertical rails as shown in the figure. There is a uniform magnetic field B0​=4 T… Includes table Includes diagram2023 · MCQ
  • Consider an LC circuit, with inductance L=0.1H and capacitance C=10−3 F, kept on a plane. The area of the circuit is 1 m2. It is placed in a constant magnetic field of strength B0​ which is…2022 · Numerical
  • The inductors of two LR circuits are placed next to each other, as shown in the figure. The values of the self-inductance of the inductors, resistors, mutual-inductance and applied voltages are specified in the given circuit. After both… Includes diagram2020 · Numerical