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A proton carrying 1 MeV kinetic energy is moving in a circular path of radius

A proton carrying 1 MeV kinetic energy is moving in a circular path of radius R in uniform magnetic field. What should be the energy of an α-particle to describe a circle of same radius in the same field?

Options

(a) 2 MeV
(b) 1 MeV
(c) 0.5 MeV
(d) 4 MeV

Correct Answer:

1 MeV

Explanation:

According to the principal of circular motion in a magnetic field
Fc = Fm ⇒ mv²/R = qvB
⇒ R = mv/qB = P/qB = √2m.k/qB
Rα = √2(4m)K’/2qB
R/Rα =√ K/K’
but R =Rα (given) Thus K=K’=1 MeV

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