A charged particle moves along circular path in a uniform magnetic field in a cyclotron. kinetic ene

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4.Moving Charges and Magnetism

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A charged particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charged particle increases to $4$ times its initial value. What will be the ratio of new radius to the original radius of circular path of the charged particle

A

$1: 1$

B

$1: 2$

C

$2: 1$

D

$1: 4$

(JEE MAIN-2022)

Solution

radius of paerticle in cyclotron

$r =\frac{\sqrt{2 mK . E .}}{ qB }$

So ratio of new radius to original

$\frac{ r _{ n }}{ r _{0}}=\sqrt{\frac{( K \cdot E .)_{ n }}{( K \cdot E )_{0}}}=\sqrt{4} \Rightarrow 2: 1$

Standard 12

Physics

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