In a magnetic field of strength 0.10 T , a proton moves in a circle of radius 1 cm . Determine the radius of the circle traced by an -particle travelling at the same speed within the same magnetic field.

Step-by-step solution

The radius of a charged particle moving in a uniform magnetic field is given by r = mv qB . Since the speed v and magnetic field B are the same for both particles, the radius is proportional to the mass-to-charge ratio: r m q For a proton, let mass be m and charge be e . Then r_ p m e . For an -particle, mass is 4m and charge is 2e . Then r_ 4m 2e = 2m e . Taking the ratio of the radii: r_ r_ p = 2m e m e = 2 Given r_ p = 1 cm , we get: r_ = 2 1 cm = 2 cm