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  4. 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 :

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Q. 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 :

JEE MainJEE Main 2022Moving Charges and Magnetism

Solution:

radius of paerticle in cyclotron
$r=\frac{\sqrt{2 mK \cdot E .}}{ qB }$
So ratio of new radius to original
$\frac{r_{n}}{r_{0}}=\sqrt{\frac{(\text { K.E. })_{n}}{(\text { K.E })_{0}}}$
$=\sqrt{4} \Rightarrow 2: 1$