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NEET 1991 (AIPMT) · Moving Charge in a Magnetic Field

Moving Charge in a Magnetic Field question from NEET 1991 (AIPMT)

Q134NEET 1991 · AIPMTMedium

Moving Charge in a Magnetic Field

A deuteron of kinetic energy 50 keV50\text{ keV} is describing a circular orbit of radius 0.50.5 metre in a plane perpendicular to magnetic field BB. The kinetic energy of the proton that describes a circular orbit of radius 0.50.5 metre in the same plane with the same BB is

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Answer: (d)

  1. Same rr and BB: K=q2B2r22m⇒K∝q2mK = \dfrac{q^2B^2r^2}{2m} \Rightarrow K \propto \dfrac{q^2}{m}.
  2. Deuteron: q=eq = e, m=2mpm = 2m_p; proton: q=eq = e, m=mpm = m_p.
  3. KpKd=2mpmp=2⇒Kp=2×50=100\dfrac{K_p}{K_d} = \dfrac{2m_p}{m_p} = 2 \Rightarrow K_p = 2 \times 50 = 100 keV
  4. So the answer is (d) 100 keV100\text{ keV}.
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