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NEET 2012 (AIPMT, Prelims) · Moving Charge in a Magnetic Field

Moving Charge in a Magnetic Field question from NEET 2012 (AIPMT, Prelims)

Q106NEET 2012 · AIPMT · PRELIMSMedium

Moving Charge in a Magnetic Field

An alternating electric field, of frequency vv, is applied across the dees (radius = R) of a cyclotron that is being used to accelerate protons (mass = m). The operating magnetic field (B) used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it, are given by

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Answer: (c)

  1. Resonance condition: ν=eB2πm⇒B=2πmνe\nu = \dfrac{eB}{2\pi m} \Rightarrow B = \dfrac{2\pi m\nu}{e}.
  2. At the edge, R=mveB⇒v=eBRm=2πνRR = \dfrac{mv}{eB} \Rightarrow v = \dfrac{eBR}{m} = 2\pi\nu R.
  3. K=12mv2=12m(2πνR)2=2mπ2ν2R2K = \tfrac{1}{2}mv^2 = \tfrac{1}{2}m(2\pi\nu R)^2 = 2m\pi^2\nu^2R^2
  4. So the answer is (c).
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