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Electromagnetic Induction question

2024 · 31 Jan · Shift 1 · Q73
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  5. /2024 · 31 Jan · Shift 1 · Q73

Electromagnetic Induction question

2024 · 31 Jan · Shift 1 · Q73

JEE MainPhysicsElectromagnetic InductionMCQ+4 / −1
A coil is places perpendicular to a magnetic field of 5000 T5000 \mathrm{~T}5000 T. When the field is changed to 3000 T3000 \mathrm{~T}3000 T in 2 s2 \mathrm{~s}2 s, an induced emf of 22 V22 \mathrm{~V}22 V is produced in the coil. If the diameter of the coil is 0.02 m0.02 \mathrm{~m}0.02 m, then the number of turns in the coil is:
  1. A
    35
  2. B
    70
  3. C
    7
  4. D
    140
View written solutionFree

Correct answer: B

  1. Use Faraday’s law

For a coil of NNN turns,

E=NΔΦΔt\mathcal{E} = N\frac{\Delta \Phi}{\Delta t}E=NΔtΔΦ​

Since the plane of the coil is perpendicular to the magnetic field, the area vector is parallel to B⃗\vec BB, so flux through one turn is

Φ=BA\Phi = BAΦ=BA

Hence,

E=NAΔBΔt\mathcal{E} = N A \frac{\Delta B}{\Delta t}E=NAΔtΔB​
  1. Given data
  • Initial magnetic field: B1=5000 TB_1 = 5000\,\text{T}B1​=5000T
  • Final magnetic field: B2=3000 TB_2 = 3000\,\text{T}B2​=3000T
  • Time interval: Δt=2 s\Delta t = 2\,\text{s}Δt=2s
  • Induced emf: E=22 V\mathcal{E} = 22\,\text{V}E=22V
  • Diameter of coil: d=0.02 md = 0.02\,\text{m}d=0.02m

So radius is

r=d2=0.01 mr = \frac{d}{2} = 0.01\,\text{m}r=2d​=0.01m
  1. Area of the coil
A=πr2=π(0.01)2=π×10−4 m2A = \pi r^2 = \pi (0.01)^2 = \pi \times 10^{-4}\,\text{m}^2A=πr2=π(0.01)2=π×10−4m2
  1. Rate of change of magnetic field
ΔB=∣B2−B1∣=∣3000−5000∣=2000 T\Delta B = |B_2 - B_1| = |3000 - 5000| = 2000\,\text{T}ΔB=∣B2​−B1​∣=∣3000−5000∣=2000T ΔBΔt=20002=1000 T/s\frac{\Delta B}{\Delta t} = \frac{2000}{2} = 1000\,\text{T/s}ΔtΔB​=22000​=1000T/s
  1. Substitute into Faraday’s law
22=N⋅π×10−4⋅100022 = N \cdot \pi \times 10^{-4} \cdot 100022=N⋅π×10−4⋅1000 22=N⋅0.1π22 = N \cdot 0.1\pi22=N⋅0.1π N=220.1π=220πN = \frac{22}{0.1\pi} = \frac{220}{\pi}N=0.1π22​=π220​

Using π≈227\pi \approx \frac{22}{7}π≈722​,

N=22022/7=220⋅722=70N = \frac{220}{22/7} = 220 \cdot \frac{7}{22} = 70N=22/7220​=220⋅227​=70
  1. Answer

The number of turns is

70\boxed{70}70​

So the correct option is B.

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