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Physics Question on Moving charges and magnetism

A cyclotron is used to accelerate protons.If the operating magnetic field is 1.0 T and the radius of the cyclotron ‘dees’ is 60 cm,the kinetic energy of the accelerated protons in MeV will be
[Use mp=1.6×10−27 kg,e=1.6×10−19C][Use\ m_p = 1.6×10^{-27}\ kg, e = 1.6×10^{-19}C]

A

12

B

18

C

16

D

32

Answer

18

Explanation

Solution

The correct answer is (B) : 18
R=mvBq=2mkBqR= \frac{mv}{Bq} = \frac{\sqrt{2mk}}{Bq}
⇒K=B2q2R22m⇒ K = \frac{B^2q^2R^2}{2m}
⇒(1.6×10−19)2×0.622×1.6×10−27 J⇒ \frac{(1.6×10^{-19})^2×0.6^2}{2×1.6×10^{-27}} \text\ J
= 18MeV