A proton projected into a magnetic field of 0.020 T moves in a helical path with a radius of 5.0 cm and a pitch of 20 cm . Determine the velocity components of the proton parallel and perpendicular to the magnetic field. Assume the proton's mass is 1.6 10⁻²⁷ kg .

Step-by-step solution

Given: Magnetic field B = 0.020 T Radius r = 5.0 cm = 0.05 m Pitch p = 20 cm = 0.20 m Mass of proton m = 1.6 10⁻²⁷ kg Charge of proton q = 1.6 10⁻¹⁹ C The radius of the helical path is given by: r = m v_ q B Solving for the perpendicular velocity component v_ : v_ = q B r m = 1.6 10⁻¹⁹ 0.020 0.05 1.6 10⁻²⁷ = 1.0 10^5 m/s The pitch of the helical path is given by: p = v_ T = v_ ( 2 m q B ) Solving for the parallel velocity component v_ : v_ = p q B 2 m = 0.20 1.6 10⁻¹⁹ 0.020 2 1.6 10⁻²⁷ v_ = 0.004 2 10^8 = 2 10^5 6.