Write down, in vector form, the relativistic equation of motion for a charged particle in the presence of a uniform magnetostatic field B = B_oẑ, and show that its Cartesian components are given by

where

and where β = ν/c. Show that the velocity and trajectory of the charged particle are given by the same formulas as in the nonrelativistic case, but with Ω_c replaced by |q| B_o/(mγ).

Transcribed Image Text:

d dt - (YU₂) = (B₁) v Vy qBo (rvy) = − ( 9B₁) ₁ d + dt d dt (70₂) = 0 Vx