A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charge particle?

Step-by-step solution

Radius of a charged particle moving in a magnetic field perpendicular to its velocity is given by, R = m v q B . m v can be written in terms of kinetic energy as m v = 2 m K E . Therefore, R = m v q B = 2 m K E q B ⇒ R ∝ K E ⇒ R 2 R 1 = K 2 K 1 = 4 1 = 2 1