Question

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 pahts will be equal. Any two charged particles having equal kinetic energies and entering a region of uniform magnetic field $\vec{ B }$ in a direction perpendicular to $\vec{ B }$, will describe circular trajectories of equal radii.

• A. If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
• B. If both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion.
• C. If Assertion is true but Reason is false.
• D. If both Assertion and Reason are false.

Answer 1

The Correct Option is C

The radius of the circular path is given by $r=\frac{m v}{q B}=\frac{\sqrt{2 m K}}{q B} ;$ where $ K=\frac{1}{2} m v^{2}$ Since $K$ and $B$ are the same for the two particles, $r \propto \frac{\sqrt{m}}{q}$. Now, the charge of an alpha particle is twice that of a proton and its mass is four times the mass of a proton, $\sqrt{m} / q$ will be the same for both particles. Hence, $r$ will be the same for both particles.