The radius of the path of a charged particle moving in a magnetic field is given by the formula:
r = mv/(qB),
where:
- r is the radius,
- m is the mass of the proton (≈ 1.67 x 10^-27 kg),
- v is the velocity of the proton (175 km/s = 175000 m/s),
- q is the charge of the proton (≈ 1.60 x 10^-19 C), and
- B is the magnetic field strength (64.6 mT = 64.6 x 10^-3 T).
Substituting the given values into the formula:
r = (1.67 x 10^-27 kg * 175000 m/s) / (1.60 x 10^-19 C * 64.6 x 10^-3 T)
This gives a radius r of approximately 0.302 meters or 30.2 cm.