Two particles #X# and # Y# having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular path of radius #R_1#, and #R_2# respectively. What is #X/Y#?

1 Answer
vrma
Mar 9, 2018

the two particles can be proton and deuteron nuclei.or such pairs whose charges are same but masses are different.

Explanation:

the two particles have same +ve charge i.e. charge of proton.

In heavy hydrogen deuteron nucleus an additional neutron is bound.so its mass is roughly 2 times the mass of a nucleon.

they are accelerated through same potential difference so their kinetic energy is same but their velocities will be different due to different masses.

# e. V = 1/2 . mass.v^2#
Therefore v(proton) = # sqrt{(2.e.V) /M} #
For Deuteron
v(deteron)= #1/sqrt(2) # . v(proton)

as the mass will change to twice its value for deuteron.

When they enter into same magnetic field region with different velocities the radius of the curved path will depend on the the masses also

#R(1)= sqrt{ Mv/(B.e)} # for proton

and

# R(2)= #sqrt {2.M.(v /sqrt(2))/(B.e) }# for deuteron.

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