A charged particle is moving in a uniform magnetic field in a circular path of radius 'R'. When the energy of the particle becomes 3 times the original, the new radius will be

Step-by-step solution

The radius of a charged particle moving in a uniform magnetic field is given by R = mv qB . The kinetic energy of the particle is E = p^2 2m , which gives the momentum p = mv = 2mE . Substituting the momentum in the radius formula, we get R = 2mE qB . This shows that R E . When the energy becomes 3 times the original, the new energy is E' = 3E . The new radius R' is given by R' = 2m(3E) qB = 3 2mE qB = 3 R . Answer: 3 R