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Question: Answered & Verified by Expert
If ' $q$ ' is electric charge, B is magnetic field, ' $R$ ' is the dee radius and ' $\mathrm{m}$ ' is the mass of ions, the kinetic energy of the ions in cyclotron is given by
PhysicsMagnetic Effects of CurrentAP EAMCETAP EAMCET 2023 (17 May Shift 1)
Options:
  • A $\frac{\mathrm{qBR}}{2 \mathrm{~m}}$
  • B $\frac{\mathrm{qBR}}{\mathrm{m}}$
  • C $\frac{\mathrm{q}^2 \mathrm{~B}^2 \mathrm{R}^2}{4 \pi \mathrm{m}}$
  • D $\frac{\mathrm{q}^2 \mathrm{~B}^2 \mathrm{R}^2}{2 \mathrm{~m}}$
Solution:
1820 Upvotes Verified Answer
The correct answer is: $\frac{\mathrm{q}^2 \mathrm{~B}^2 \mathrm{R}^2}{2 \mathrm{~m}}$
$\mathrm{R}=\frac{\mathrm{mv}}{\mathrm{qB}} ; \mathrm{P}=\mathrm{RqB}$
The kinetic energy of ions in cyclotron is given by
$K . E=\frac{P^2}{2 m}=\frac{q^2 R^2 B^2}{2 m}$

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