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

2020 · 5 Sep · Shift 2 · Q58
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 Main
  3. /Physics
  4. /Electromagnetic Induction
  5. /2020 · 5 Sep · Shift 2 · Q58

Electromagnetic Induction question

2020 · 5 Sep · Shift 2 · Q58

JEE MainPhysicsElectromagnetic InductionMCQ+4 / −1
An infinitely long, straight wire carrying current I, one side opened rectangular loop and a conductor C with a sliding connector are located in the same plane, as shown, in the figure. The connector has length lll and resistance R. It slides to the right with a velocity v. The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation r, between the connector and the straight wire is : JEE Main 2020 (Online) 5th September Evening Slot Physics - Electromagnetic Induction Question 82 English
  1. A
    μ04πIvlRr{{{\mu _0}} \over {4\pi }}{{Ivl} \over {Rr}}4πμ0​​RrIvl​
  2. B
    μ0πIvlRr{{{\mu _0}} \over {\pi }}{{Ivl} \over {Rr}}πμ0​​RrIvl​
  3. C
    μ02πIvlRr{{{\mu _0}} \over {2\pi }}{{Ivl} \over {Rr}}2πμ0​​RrIvl​
  4. D
    2μ0πIvlRr{{2{\mu _0}} \over \pi }{{Ivl} \over {Rr}}π2μ0​​RrIvl​
View written solutionFree

Correct answer: C

  1. Magnetic field due to the long straight wire

At a perpendicular distance rrr from an infinitely long straight wire carrying current III, the magnetic field is

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

  1. Flux change due to motion of the sliding connector

The sliding rod/connector of length lll moves to the right with speed vvv. The loop is completed by this rod, so as it moves, the area of the loop changes.

Since the magnetic field is perpendicular to the plane of the loop and has magnitude B(r)B(r)B(r) at the rod location, the motional emf induced across the rod is

E=B(r) l v.\mathcal E = B(r)\, l\, v.E=B(r)lv.

Substituting B(r)B(r)B(r):

E=μ0I2πr lv.\mathcal E = \frac{\mu_0 I}{2\pi r}\, l v.E=2πrμ0​I​lv.

  1. Induced current in the loop

The only resistance in the circuit is the resistance RRR of the sliding connector. Hence, by Ohm’s law,

i=ER=1R⋅μ0Ilv2πr.i = \frac{\mathcal E}{R} = \frac{1}{R}\cdot \frac{\mu_0 I l v}{2\pi r}.i=RE​=R1​⋅2πrμ0​Ilv​.

Therefore,

i(r)=μ02πIvlRr.i(r)=\frac{\mu_0}{2\pi}\frac{Ivl}{Rr}.i(r)=2πμ0​​RrIvl​.

  1. Matching with options

This matches Option C:

μ02πIvlRr.\boxed{\frac{\mu_0}{2\pi}\frac{Ivl}{Rr}}.2πμ0​​RrIvl​​.

PreviousNext

More from Electromagnetic Induction

  • A part of a complete circuit is shown in the figure. At some instant, the value of current I is 1A and it is decreasing at a rate of 102 A s–1. The value of the potential difference VP – VQ , (in volts) at that instant, is ​… Includes diagram2020 · Numerical
  • A long solenoid of radius R carries a time (t) - dependent current I(t)=I0t(1 - t). A ring of radius 2R is placed coaxially near its middle. During the time interval 0 ≤ t ≤ 1, the induced current (IR) and the induced EMF(VR) in…2020 · MCQ
  • 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 i. The magnetic…2020 · MCQ
  • A loop ABCDEFA of straight edges has six corner points A(0, 0, 0), B(5, 0, 0), C(5, 5, 0), D (0, 5, 0), E(0, 5, 5) and F(0, 0, 5). The magnetic field in this region is B=(3i+4k)T .…2020 · Numerical
  • A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the magnitude of induced emf…2020 · MCQ
  • At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next 5s, then induced EMF in the loop is : Includes diagram2020 · MCQ
  • A shown in the figure, a battery of emf ε is connected to an inductor L and resistance R in series. The switch is closed at t = 0. The total charge that flows from the battery, between t = 0 and t = tc (tc is the time constant… Includes diagram2020 · MCQ
  • In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25 A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be ​…2020 · Numerical