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Universal Law of Gravitation

A proton , a ...

Question

A proton , a deuteron , a alpha particle having same kinetic energy enter perpendicular to a uniform magnetic field . find ratio of radii circular paths ?

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Solution

$F o r c e a c t i n g i n t h e m a g n e t i c f i e l d i s g i e v n b y : F = q V B \frac{m v^{2}}{r} = q v B r = \frac{m v}{q B} w h e r e r i s t h e r a d i u s o f t h e c i r c u l a r p a t h P = m v k i n e t i c e n e g r y = \frac{p^{2}}{2 m} p = \sqrt{2 m \times K E} r = \frac{\sqrt{2 m \times K E}}{q B} q_{p} = e q_{d} = e q_{a} = 2 e m_{p} = m m_{d} = 2 m m_{a} = 4 m r_{p} = \frac{\sqrt{2 m \times K E}}{e B} r_{d} = \frac{\sqrt{4 m \times K E}}{e B} r_{a} = \frac{\sqrt{8 m \times K E}}{2 e B} r_{p} : r_{d} : r_{a} = \sqrt{2} : 2 : \sqrt{2} = 1 : \sqrt{2} : 1$

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