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Magnetics question

2022 · 29 Jul · Shift 1 · Q72
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  5. /2022 · 29 Jul · Shift 1 · Q72

Magnetics question

2022 · 29 Jul · Shift 1 · Q72

JEE MainPhysicsMagneticsNumerical+4 / −1
A closely wounded circular coil of radius 5 cm produces a magnetic field of 37.68×10−4 T37.68 \times 10^{-4} \mathrm{~T}37.68×10−4 T at its center. The current through the coil is ‾\underline{\hspace{2cm}}​ A. [Given, number of turns in the coil is 100 and π=3.14\pi=3.14π=3.14]
Numerical answer
View written solutionFree

Correct answer: 3

  1. Magnetic field at the center of a circular coil

For a coil of NNN turns and radius RRR, carrying current III, the magnetic field at the center is

B=μ0NI2RB = \frac{\mu_0 N I}{2R}B=2Rμ0​NI​

where

μ0=4π×10−7 T m A−1\mu_0 = 4\pi \times 10^{-7}\ \text{T m A}^{-1}μ0​=4π×10−7 T m A−1
  1. Given data
  • Radius: R=5 cm=0.05 mR = 5\text{ cm} = 0.05\text{ m}R=5 cm=0.05 m
  • Number of turns: N=100N = 100N=100
  • Magnetic field:
B=37.68×10−4 T=3.768×10−3 TB = 37.68 \times 10^{-4}\ \text{T} = 3.768 \times 10^{-3}\ \text{T}B=37.68×10−4 T=3.768×10−3 T
  • π=3.14\pi = 3.14π=3.14
  1. Substitute into the formula
3.768×10−3=(4π×10−7)(100)I2(0.05)3.768 \times 10^{-3} = \frac{(4\pi \times 10^{-7})(100)I}{2(0.05)}3.768×10−3=2(0.05)(4π×10−7)(100)I​

Since

2(0.05)=0.12(0.05)=0.12(0.05)=0.1

we get

3.768×10−3=4π×10−5I0.13.768 \times 10^{-3} = \frac{4\pi \times 10^{-5} I}{0.1}3.768×10−3=0.14π×10−5I​ 3.768×10−3=4π×10−4I3.768 \times 10^{-3} = 4\pi \times 10^{-4} I3.768×10−3=4π×10−4I
  1. Now solve for III
I=3.768×10−34π×10−4I = \frac{3.768 \times 10^{-3}}{4\pi \times 10^{-4}}I=4π×10−43.768×10−3​ I=3.768×10−34×3.14×10−4I = \frac{3.768 \times 10^{-3}}{4 \times 3.14 \times 10^{-4}}I=4×3.14×10−43.768×10−3​ I=3.768×10−312.56×10−4I = \frac{3.768 \times 10^{-3}}{12.56 \times 10^{-4}}I=12.56×10−43.768×10−3​ I=3.7681.256I = \frac{3.768}{1.256}I=1.2563.768​ I=3I = 3I=3
  1. Final answer

The current through the coil is

3 A\boxed{3\ \text{A}}3 A​
  1. Comparison with stored correct answer

Stored correct answer: 333

My derived answer is also 333, so they agree.

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