Question

a beam of protons and deuterons, each having the same momentum, enters a region of
uniform magnetic field directed perpendicular to their direction of momentum. What would be the
ratio of the circular paths described by them?​

Answer 1

Answer:

Let r be the radius.

Let b be the magnetic field.

Let m be the mass.

Let v be the velocity

Let q be the charge.

We know that:

By equating centripetal force and Lorentz force. Thus by simplifying we get:

Momentum of both proton and deuteron is same as it is given to us.

A deuteron is a particle one proton and one neutron. Hence the charge on both proton and deuteron is same.

Now as momentum is same, charge is same and the magnetic field is also same, the radii of both are also same.

Hence ratio of radii of proton and deuteron is 1:1