Question

A proton, dutrium and an alpha particle enter a magnetic field perpendicular to the field with same velocities. Then what is the ratio of the radii of their paths ?

Answer 1

Dear Student ,
Here in this case ,a proton , a deuterium and an alpha particle enters in a magnetic field perpendicular with field with same velocities .
$$\begin{gathered} Here,weknowthat, \\ qvB=\frac{m{v}^2}{r} \\ \Rightarrow r=\frac{mv}{qB} \\ Nowlook,theratioof\frac{v}{B}iscons\tan tasvandBaresameforalltheparticles. \\ So,themassoftheproton,m_p=1,chargeofproton,q_p=1 \\ themassofthedeuterium,m_d=2,chargeofproton,q_d=1 \\ themassofthealphaparticle,m_{\alpha }=4,chargeofalphaparticle,q_{\alpha }=2 \\ Now,r_p:r_d:r_{\alpha }=\frac{m_p}{q_p}:\frac{m_d}{q_d}:\frac{m_{\alpha }}{q_{\alpha }}=\frac{1}{1}:\frac{2}{1}:\frac{4}{2}=1:2:2 \end{gathered}$$
Regards