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.

Answer 1

We know, Lorentz force, F = Bqv sinθ

where θ = angle between velocity of particle and magnetic field = 90^o

So, Lorentz force, F = Bqv

Thus the particles will move in circular path.

`Bqv = (mv^2)/r ⇒ r = (mv)/(Bq)`

Let m_p = mass of proton, m_d = mass of deuteron, v_p = velocity of proton and

v_d = velocity of deuteron

The charge of proton and deuteron are equal.

Given that m_p v_p = m_d v_d

`r_p= (m_pv_p)/(Bq)`  ................ (1)`

`r_d= (m_dv_d)/(Bq)`  ................ (1)`

As (1) and (2) are equal , so r_p = r_d = r

Thus, the trajectory of both the particles will be same.