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NEET 1996 (AIPMT) · Moving Charge in a Magnetic Field

Moving Charge in a Magnetic Field question from NEET 1996 (AIPMT)

Q130NEET 1996 · AIPMTEasy

Moving Charge in a Magnetic Field

A 10 eV10\text{ eV} electron is circulating in a plane at right angles to a uniform field at magnetic induction 10−4 Wb/m210^{-4}\text{ Wb/m}^2 (= 1.0 gauss), the orbital radius of electron is

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Answer: (a)

  1. r=mveB=2mKeBr = \dfrac{mv}{eB} = \dfrac{\sqrt{2mK}}{eB}
  2. K=10 eV=1.6×10−18 JK = 10\text{ eV} = 1.6\times10^{-18}\text{ J}, m=9.1×10−31 kgm = 9.1\times10^{-31}\text{ kg}
  3. 2mK=2×9.1×10−31×1.6×10−18≈1.71×10−24\sqrt{2mK} = \sqrt{2\times9.1\times10^{-31}\times1.6\times10^{-18}} \approx 1.71\times10^{-24}
  4. r=1.71×10−241.6×10−19×10−4≈0.107 mr = \dfrac{1.71\times10^{-24}}{1.6\times10^{-19}\times10^{-4}} \approx 0.107\text{ m}
  5. So the answer is (a) ≈11 cm\approx 11\text{ cm}.
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