Consider the motion of an electron in the presence of a uniform magnetostatic field B = B₀ẑ, and an electric field that oscillates in time at the electron cyclotron frequency Ω_c, according to

(a) What type of polarization has this electric field?

(b) Obtain the following uncoupled differential equations satisfied by the velocity components v_x(t) and v_y(t):

(c) Assume that, at t = 0, the electron is located at the origin of the coordinate system, with zero velocity. Neglect the time-varying part of B. Show that the electron velocity is given by

(d) Show that the electron trajectory is given by

Transcribed Image Text:

E(t) = Eo(x cos Net + y sin Net)