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QJEEAdv21Pha8c1: JEE Advanced 2021 Physics - Class 12 JEEAdv21Pha8c1 Solution: An -particle (mass 4 amu) and a singly charged sulphur ion…

An α\alpha -particle (mass 4 amu) and a singly charged sulphur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the α\alpha -particle and the sulfur ion move in circular orbits of radii r α\alpha and rs, respectively. The ratio (rs/r α\alpha ) is __________.

Step-by-Step Verified Solution

rα=2mαqαVqαB{r_\alpha } = {{\sqrt {2{m_\alpha }{q_\alpha }V} } \over {{q_\alpha }B}}

rs=2msqsVqsB{r_s} = {{\sqrt {2{m_s}{q_s}V} }\over {{q_s}B}}

rsrα=msqsqαmα=(321)(24){{{r_s}} \over {{r_\alpha }}} = \sqrt {{{{m_s}} \over {{q_s}}}{{{q_\alpha }} \over {{m_\alpha }}}} = \sqrt {\left( {{{32} \over 1}} \right)\left( {{2 \over 4}} \right)}

rsrα=4{{{r_s}} \over {{r_\alpha }}} = 4

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