A proton, a deuteron, and α-particle are accelerated through same potential difference and then enter in a uniform perpendicular magnetic - Physics - Moving Charges And Magnetism

Question

A proton, a deuteron, and α-particle are accelerated through
same potential difference and then enter in a uniform perpendicular
magnetic field Find the ratio of their radii?

Vaibhav T. · Accepted Answer

Dear Student,

We know that,qvB=mv2RR=mvqB  
 1Also, according to conservation of energy, PE=qVwhere, V=potential difference12mv2=qVv=2qVm  
 2from 1 and 2, we get,R=mqB×2qVmR=B2V×mqSince B and V are same for all charges, the ratio is,Rp:Rd:Rα=mpqp:mdqd:mαqαWe aso know that,md=2mp and mα=4mpqd=qp and qα=2qpRp:Rd:Rα=mpqp:2mpqp:4mp2qpRp:Rd:Rα=mpqp1:2:4Rp:Rd:Rα=1:2:2

A proton, a deuteron, and α-particle are accelerated through same potential difference and then enter in a uniform perpendicular magnetic field. Find the ratio of their radii?