a proton and an alpha particle move perpendicular to a magnetic field.Find the ratio of radii of the circular paths described by them when both have equal momenta?
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When a charged particle ( of charge 'q' and mass 'm' ) having velocity 'v' enters perpendicularly in a magnetic field (B) . A magnetic force act on it which is perpendicular to both 'v' and 'B' and due to it the particle describes a circular path of radius 'r' given by :
r= mv /qB
=> r = p/qB
here 'p' is momentum ;p= mv .
_________________
As momenta are same and B for both is also same .
=> r is proportional to 1/q
=>
r(alpha) /r(proton) = q(proton)/q(alpha)
= 1/2
(as charge on alpha particle is twice that of proton )
__________________
hope it helps !!
r= mv /qB
=> r = p/qB
here 'p' is momentum ;p= mv .
_________________
As momenta are same and B for both is also same .
=> r is proportional to 1/q
=>
r(alpha) /r(proton) = q(proton)/q(alpha)
= 1/2
(as charge on alpha particle is twice that of proton )
__________________
hope it helps !!
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