A stream of protons is moving in the +x direction. They enter a magnetic field o

Question

A stream of protons is moving in the +x direction. They enter a magnetic field of magnitude 0.040 T that points in the +z direction. The magnetic field extends from x=0 to x=1.0 m. The protons exit the magnetic field (at the x=1.0 m side of the field), still moving in the +x direction but they now also have some y-directed motion. Find the y-component of a proton’s momentum as it leaves the magnetic field. (Ignore any gravitational effects/forces.) Interestingly, you don’t need to know the original velocity or mass of the proton to answer this! q+ = 1.60x10-19 C

Explanation / Answer

Lorentz force acts perpendicular to motion changing its direction but not the speed

=> qvB = mv2/r

=> r = mv/qB

=>    y-component of a proton’s momentum =   sin(theta) *mv

                                                                        = (1/r) * mv

                                                                         =   q B

                                                                          = 1.6 * 10-19 * 0.040

                                                                          = 6.4 * 10-21 kg-m/sec

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