Verified Solution • 2025–26 Session moderate

QAIPM-2012-Ph-1744: NEET 2012 Physics - Class 12 AIPM-2012-Ph-1744 Solution: An alternating electric field, of frequency \( \), is applied…

An alternating electric field, of frequency ν\nu, 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

Multiple Choice Options

  • A B=mνeB=\frac{m\nu}{e} and K=2mπ2ν2R2K=2m\pi^2\nu^2R^2
  • B B=2πmνeB=\frac{2\pi m\nu}{e} and K=m2πνR2K=m^2\pi\nu R^2
  • C B=2πmνeB=\frac{2\pi m\nu}{e} and K=2mπ2ν2R2K=2m\pi^2\nu^2R^2
  • D B=mνeB=\frac{m\nu}{e} and K=m2πνR2K=m^2\pi\nu R^2

Step-by-Step Verified Solution

Time period of cyclotron is T = 1 v = 2 � m e B ; B = 2 � m e v ; R = m v e B = p e B _ P = e B R = e _ 2 � m v e R = 2 � m v R K . E . = p 2 2 m = ( 2 � m v R ) 2 2 m = 2 � 2 m v 2 R 2

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