The ratio of cyclotron frequency f to the radius of the path of a charged particle R is q^2 B^2 2 m^2 x . Then the value of x is ( v is velocity of charged particle)

Step-by-step solution

The radius of the circular path of a charged particle in a uniform magnetic field is given by R = mv qB . The cyclotron frequency is given by f = qB 2 m . Taking the ratio of the cyclotron frequency to the radius, we get: f R = qB 2 m mv qB = q^2 B^2 2 m^2 v It is given that f R = q^2 B^2 2 m^2 x . Comparing the two expressions, we get x = 1 v = v⁻¹ . Answer: v⁻¹