A proton and an α -particle, moving with the same velocity, enter into a uniform magnetic field, acting normal to the plane of their motion. The ratio of the radii of the circular paths described by t

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A proton and an α -particle, moving with the same velocity, enter into a uniform magnetic field, acting normal to the plane of their motion. The ratio of the radii of the circular paths described by the proton and α -particle is

TestHub · Accepted Answer

While describing circular path, the centripetal and centrifugal forces are balancing each other. ⇒ r m v 2 ​ = q v B (as the uniform magnetic field is acting normal to the plane) ​ ⇒ r = qB m v ​ ⇒ r α ​ r p ​ ​ = e B m p ​ v ​ × m α ​ v 2 e B ​ = 4 m p ​ 2 m p ​ ​ [ as m α ​ = 4 m p ​ ] ∴ r p ​ : r α ​ = 1 : 2 ​

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