Final answer:
The radius of the proton's circular path is approximately 2.85 × 10^-4 m.
Step-by-step explanation:
To find the radius of the circular path, we can use the equation for the centripetal force experienced by a charged particle moving in a magnetic field. The centripetal force is provided by the magnetic force:
F = qvB
where F is the magnetic force, q is the charge of the particle, v is its velocity, and B is the magnetic field.
Since the particle is moving in a circular path, the magnetic force is equal to the centripetal force:
F = mv^2 / r
where m is the mass of the particle and r is the radius of the circular path.
Since the charge of a proton is 1.602 × 10^-19 C and its mass is 1.67 × 10^-27 kg, we can rearrange the equations and solve for the radius:
r = mv / qB
Plugging in the given values:
r = (1.67 × 10^-27 kg) × (4.8×10^-16 J) / (1.602 × 10^-19 C) × (0.34 T)
r ≈ 2.85 × 10^-4 m
Therefore, the radius of the proton's circular path is approximately 2.85 × 10^-4 m.