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Question
A proton and a deuteron having equal momenta enter in a region of a uniform magnetic field at right angle to the direction of a the field. Depict their trajectories in the field.
Solution
We know, Lorentz force, F = Bqv sinθ
where θ = angle between velocity of particle and magnetic field = 90o
So, Lorentz force, F = Bqv
Thus the particles will move in circular path.
`Bqv = (mv^2)/r ⇒ r = (mv)/(Bq)`
Let mp = mass of proton, md = mass of deuteron, vp = velocity of proton and
vd = velocity of deuteron
The charge of proton and deuteron are equal.
Given that mp vp = md vd
`r_p= (m_pv_p)/(Bq)` ................ (1)`
`r_d= (m_dv_d)/(Bq)` ................ (1)`
As (1) and (2) are equal , so rp = rd = r
Thus, the trajectory of both the particles will be same.
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