Question

A proton , a deuteron , a alpha particle having same kinetic energy enter perpendicular to a uniform magnetic field . find ratio of radii circular paths ?

Answer 1

$$\begin{gathered} Forceactinginthemagneticfieldisgievnby: \\ F\hspace{0.17em}=qVB \\ \frac{m{v}^2}{r}=qvB \\ r=\frac{mv}{qB} \\ whereristheradiusofthecircularpath \\ P=mv \\ kineticenegry=\frac{p^2}{2m} \\ p=\sqrt{2m\times KE} \\ r=\frac{\sqrt{2m\times KE}}{qB} \\ {q}_p=e \\ {q}_d=e \\ {q}_a=2e \\ {m}_p=m \\ {m}_d=2m \\ {m}_a=4m \\ {r}_p=\frac{\sqrt{2m\times KE}}{eB} \\ {r}_d=\frac{\sqrt{4m\times KE}}{eB} \\ {r}_a=\frac{\sqrt{8m\times KE}}{2eB} \\ {r}_p:r_d:r_a=\sqrt{2}:2:\sqrt{2}=1:\sqrt{2}:1 \end{gathered}$$