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

2022 · 24 Jun · Shift 2 · Q69
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. /2022 · 24 Jun · Shift 2 · Q69

Electromagnetic Induction question

2022 · 24 Jun · Shift 2 · Q69

JEE MainPhysicsElectromagnetic InductionNumerical+4 / −1
A circular coil of 1000 turns each with area 1m2 is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of 0.07T. The maximum voltage generation will be ‾\underline{\hspace{2cm}}​ V.
Numerical answer
View written solutionFree

Correct answer: 440

  1. Given data
  • Number of turns: N=1000N = 1000N=1000
  • Area of each turn: A=1 m2A = 1\,\text{m}^2A=1m2
  • Magnetic field: B=0.07 TB = 0.07\,\text{T}B=0.07T
  • Rotation rate: f=1 rev/sf = 1\,\text{rev/s}f=1rev/s

The coil rotates about its vertical diameter in a horizontal magnetic field, so the angle between the area vector and magnetic field changes with time.

  1. Magnetic flux through the coil

For a rotating coil,

Φ=NBAcos⁡(ωt)\Phi = NBA\cos(\omega t)Φ=NBAcos(ωt)

where angular speed

ω=2πf=2π×1=2π rad/s\omega = 2\pi f = 2\pi \times 1 = 2\pi\,\text{rad/s}ω=2πf=2π×1=2πrad/s
  1. Induced emf

By Faraday's law,

e=−dΦdte = -\frac{d\Phi}{dt}e=−dtdΦ​

So,

e=NBAωsin⁡(ωt)e = NBA\omega \sin(\omega t)e=NBAωsin(ωt)

Hence the maximum emf is

emax⁡=NBAωe_{\max} = NBA\omegaemax​=NBAω
  1. Substitute values
emax⁡=1000×0.07×1×2πe_{\max} = 1000 \times 0.07 \times 1 \times 2\piemax​=1000×0.07×1×2π emax⁡=70×2π=140πe_{\max} = 70 \times 2\pi = 140\piemax​=70×2π=140π emax⁡≈140×3.14=439.6 Ve_{\max} \approx 140 \times 3.14 = 439.6\,\text{V}emax​≈140×3.14=439.6V

Therefore,

emax⁡≈440 Ve_{\max} \approx 440\,\text{V}emax​≈440V
  1. Final answer

The maximum voltage generated is

440\boxed{440}440​
PreviousNext

More from Electromagnetic Induction

  • A small square loop of wire of side l is placed inside a large square loop of wire L(L>>l). Both loops are coplanar and their centres coincide at point O as shown in figure. The mutual inductance of… Includes diagram2022 · MCQ
  • The electric current in a circular coil of 2 turns produces a magnetic induction B1 at its centre. The coil is unwound and in rewound into a circular coil of 5 tuns and the same current produces a magnetic induction B2 at its centre. The…2022 · MCQ
  • Magnetic flux (in weber) in a closed circuit of resistance 20 Ω varies with time t(s) at ϕ= 8t2 − 9t + 5. The magnitude of the induced current at t = 0.25 s will be ​ mA.2022 · Numerical
  • The current in a coil of self inductance 2.0 H is increasing according to I = 2 sin(t2) A. The amount of energy spent during the period when current changes from 0 to 2 A is ​ J.2022 · Numerical
  • In a coil of resistance 8Ω, the magnetic flux due to an external magnetic field varies with time as ϕ=32​(9−t2). The value of total heat produced in the coil, till the flux becomes zero, will be ​J…2022 · Numerical
  • The magnetic flux through a coil perpendicular to its plane is varying according to the relation ϕ=(5t3+4t2+2t−5) Weber. If the resistance of the coil is 5 ohm, then the induced current through the coil at t = 2 s will…2022 · MCQ
  • A 10 Ω, 20 mH coil carrying constant current is connected to a battery of 20 V through a switch. Now after switch is opened current becomes zero in 100 μ s. The average e.m.f. induced in the coil is ​ V.2022 · Numerical
  • Two coils of self inductance L1 and L2 are connected in series combination having mutual inductance of the coils as M. The equivalent self inductance of the combination will be : Includes diagram2022 · MCQ