Assertion 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. Reason Any two charged particles having equal kinetic energies and entering a region of uniform magnetic field mathbf vecB in a direction perpendicular to mathbf vecB , will describe circular trajectories of equal radii.

Question

Assertion 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. Reason Any two charged particles having equal kinetic energies and entering a region of uniform magnetic field mathbf vecB in a direction perpendicular to mathbf vecB , will describe circular trajectories of equal radii. (A) If the Assertion and Reason are true and Reason is the correct explanation of Assertion. (B) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. (C) If Assertion is true but Reason is false. (D) If both Assertion and Reason are false.

Tardigrade Admin · Accepted Answer

The radius of the circular path is given by r=(mv/qB)=(√2mK/qB); where K=(1/2)mv2 Since K and B are the same for the t particles, r propto (√m/q). 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 both particles. Hence, r will be same for both particles.