To find the magnitude of the force that the magnetic field exerts on the proton, we can use the formula:
F = qvBsinθ
where F is the force, q is the charge of the particle (in this case, a proton with a charge of +1.602 x 10^-19 C), v is the velocity of the particle, B is the magnetic field strength, and θ is the angle between the velocity vector and the magnetic field vector.
Plugging in the values given, we get:
F = (1.602 x 10^-19 C)(3.70 x 10^3 m/s)(0.710 T)sin(55°)
F ≈ 1.51 x 10^-14 N
Therefore, the magnitude of the force that the magnetic field exerts on the proton is approximately 1.51 x 10^-14 N.