The cyclotron is designed to accelerate protons to an energy of 5 MeV. Determine the largest radius of the orbit

The cyclotron is designed to accelerate protons to an energy of 5 MeV. Determine the largest radius of the orbit along which the proton moves, if the magnetic induction is 4 T.

The kinetic energy is equal to the product of 5 MV (megavol) by the electron charge:
Eк = 5 MeV = 5 * 10 (6) eV = 5×10 * (6) x 1.6×10 * (- 19) = 8×10 * (- 13) J
From the formula:
Ek = m x V (square) / 2
we find:
V = √ ((2 x E) / m) = √ (2 x 8×10 * (- 13) J / 1.67×10 * (- 27) ≈ 3.1×10 * (7) m / s
2) The Lorentz force acting on the proton is equal to the centripetal force:
q x B x V = (m x V * (2)) / R
R = m x V / (q x B) = 1.67×10 * (- 27) x 3.1×10 * (7) / (1.6×10 * (- 19) x 4) = 0.081 m