Verified Solution • 2025–26 Session moderate

QJEEM22Phea52: JEE Main 2022 Physics - Class 12 JEEM22Phea52 Solution: A cyclotron is used to accelerate protons. If the operating…

A cyclotron is used to accelerate protons. If the operating magnetic field is 1.0 T1.0 \mathrm{~T} and the radius of the cyclotron 'dees' is 60 cm60 \mathrm{~cm} , the kinetic energy of the accelerated protons in MeV will be :

[use  mp=1.6×10−27 kg,e=1.6×10−19 C[\mathrm{use} \,\,\mathrm{m}_{\mathrm{p}}=1.6 \times 10^{-27} \mathrm{~kg}, \mathrm{e}=1.6 \times 10^{-19} \,\mathrm{C} ]

Multiple Choice Options

  • A 12
  • B 18
  • C 16
  • D 32

Step-by-Step Verified Solution

R=mvBq=2mKBqR = {{mv} \over {Bq}} = {{\sqrt {2mK} } \over {Bq}}

⇒K=B2q2R22m\Rightarrow K = {{{B^2}{q^2}{R^2}} \over {2m}}

=(1.6×10−19)2×0.622×1.6×10−27= {{{{(1.6 \times {{10}^{ - 19}})}^2} \times {{0.6}^2}} \over {2 \times 1.6 \times {{10}^{ - 27}}}} J

=18= 18 MeV

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