(C) The radius $r$ of a charged particle moving in a uniform magnetic field $B$ is given by $r = \frac{mv}{qB} = \frac{\sqrt{2mK}}{qB}$,where $K$ is t

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(C) The radius $r$ of a charged particle moving in a uniform magnetic field $B$ is given by $r = \frac{mv}{qB} = \frac{\sqrt{2mK}}{qB}$,where $K$ is the kinetic energy.For a proton,$m_p = m$ and $q_p = e$. Thus,$r_p = \frac{\sqrt{2mK}}{eB}$.For an alpha particle,$m_{\alpha} = 4m$ and $q_{\alpha} = 2e$. Thus,$r_{\alpha} = \frac{\sqrt{2(4m)K}}{(2e)B} = \frac{2\sqrt{2mK}}{2eB} = \frac{\sqrt{2mK}}{eB}$.Since $r_p = r_{\alpha}$,the Assertion is correct.The Reason states that any two charged particles with equal kinetic energies in a uniform magnetic field will have equal radii. However,the radius depends on the ratio $\frac{\sqrt{m}}{q}$. Since this ratio is not the same for all particles (e.g.,for an electron and a proton),the Reason is incorrect.

Class 12 Physics Moving Charges and Magnetism Motion of Charged Particle In Magnetic Field

Medium

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 $\overrightarrow{B}$ in a direction perpendicular to $\overrightarrow{B}$,will describe circular trajectories of equal radii.

AIIMS 2009 All AIIMS

A
If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B
If both Assertion and Reason are correct,but Reason is not the correct explanation of Assertion.
C
If Assertion is correct but Reason is incorrect.
D
If both the Assertion and Reason are incorrect.