Final answer:
To calculate the radius of curvature for a proton in a magnetic field, one needs to know the kinetic energy, charge, and mass of the proton, as well as the magnetic field strength. The radius can be found by using the relationship between kinetic energy and velocity, and then using that velocity in the formula that relates charge, mass, velocity, and magnetic field strength.
Step-by-step explanation:
To find the radius of curvature of the path of a 1.2 MeV proton moving perpendicularly to a 0.38 T magnetic field, we can use the formula for the radius r of the circular motion of a charged particle in a magnetic field:
r = mv/qB
where:
- m is the mass of the proton,
- v is the velocity of the proton,
- q is the charge of the proton,
- B is the magnetic field strength.
To find v, we solve the equation for kinetic energy (KE = 1/2 mv²) for velocity:
v = √(2KE/m)
We know the mass of a proton (m) is approximately 1.67 x 10⁻²⁷ kg and the charge (q) is 1.602 x 10⁻ C. Plugging in the kinetic energy in joules (1 eV = 1.602 x 10⁻ J, so 1.2 MeV = 1.2 x 10⁶ x 1.602 x 10⁻ J) and the known values, we can calculate the velocity first and then find the radius r.