In to a uniform transverse magnetic field, two charged particles having the same mass and charge enter and move in two different circular paths. The ratio of the radii of curvatures of the circular paths is 1: 4 . What would be the ratio of their respective velocities?

Step-by-step solution

The radius r of the circular path of a charged particle moving in a uniform transverse magnetic field B is given by the formula r = mv qB , where m is the mass, v is the velocity, and q is the charge of the particle. Given that the mass m and charge q are the same for both particles, and the magnetic field B is uniform, the radius r is directly proportional to the velocity v . That is, r v . Therefore, the ratio of the radii of the two circular paths is equal to the ratio of their respective velocities: r₁ r₂ = v₁