Statement $$1$$: A proton and an alpha particle having the same kinetic energy are moving in circular paths in a uniform magnetic field. The radii of their circular paths will be equal.Statement $$2$$: Any two charged particles having equal kinetic energies and entering a region of uniform magnetic field B→ in a direction perpendicular to B→, will describe circular trajectories of equal radii.

Question

Statement $$1$$: A proton and an alpha particle having the same kinetic energy are moving in circular paths in a uniform magnetic field. The radii of their circular paths will be equal.Statement $$2$$: Any two charged particles having equal kinetic energies and entering a region of uniform magnetic field B→ in a direction perpendicular to B→, will describe circular trajectories of equal radii.

Infinity Learn · Accepted Answer

The radius of the circular path is given $$byr=mvqB$$ $$=$$  $$2mKqB$$  ;   where  $$K=12$$  $$mv2Since$$ K and B are the same for the two particles, r ∝  mq.  Now, the charge of an alpha particle is twice that of a proton and its mass is four times the mass of a proton, $$m/q$$ will be the same for body particles. Hence, r will be the same for both particles.

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