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AIIMS 2005
Exam
AIIMS
Year
2005
Subject
Physics
Chapter
Electromagnetic Induction

AIIMS 2005 · Physics · Electromagnetic Induction

A conducting ring of radius 1 meter is placed in a uniform magnetic...

A conducting ring of radius 1 meter is placed in a uniform magnetic field BB of 0.01 tesla oscillating with frequency 100 Hz100 \mathrm{~Hz} with its plane at right angle to BB. What will be the induced electric field?A conducting ring of radius 1 meter is placed in a uniform magnetic field B of 0.01 tesla oscillating with frequencyA conducting ring of radius 1 meter is placed in a uniform magnetic field B of 0.01 tesla oscillating with frequency

Options

  1. Aπ\pi volts /m/ \mathrm{m}
  2. B2 volts /m/ \mathrm{m}
  3. C10 volts /m/ \mathrm{m}
  4. D62 volts /m/ \mathrm{m}.

Correct answer

B. 2 volts /m/ \mathrm{m}

Step-by-step solution

As a constant magnetic field conducting ring oscillates with a frequency of 100 Hz100 \mathrm{~Hz}. i.e. T=1100 sT=\frac{1}{100} \mathrm{~s}, for T2\frac{T}{2}, it goes up to B∴B\therefore The corresponding frequency is 200 Hz200 \mathrm{~Hz}.  Induced emf = change in  flux  time =2BAcos⁡θT=2BAfcos⁡θ=\pir2×2×0.01×200 as r=1 m=π12×2×0.01×200=4πV.\begin{aligned}& \text{ Induced emf }=\frac{\text{ change\text{ in } flux }}{\text{ time }}\\ & =\frac{2 B A \cos \theta}{T}=2 B A f \cos \theta\\ & =\pir^2 \times2 \times0.01 \times200 \text{ as }r=1 \mathrm{~m}\\ & =\pi1^2 \times2 \times0.01 \times200=4 \pi \mathrm{V} . \end{aligned}A conducting ring of radius 1 meter is placed in a uniform magnetic field B of 0.01 tesla oscillating with frequencyNon−electrostaticinducedelectricfieldalongthecircle,E=\\ Non-electrostatic induced electric field along the circle, E=\frac{1}{2 \pi r} \times\left(\pir2r^2\times \frac{d B}{d t}\right)=\frac{e}{2 \pi r}=\frac{4 \pi}{2 \pi r}=22\mathrm{~V}//\mathrm{m} .$
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