Question

A particle with charge q exists in a region with a uniform electric field Ē = Eî. There is no magnetic field. The particle’s initial velocity is ū = voĉ. The initial position is at the origin. a. Write the differential equation of motion using Newton's second law. Write it in vector form, and then write an equation for each component. b. Find x(t), y(t), and z(t).

Answer 1

Solution in the uploaded images

Solution e z → 2 q ace From the given diagram Force, Fe will be towards acting x anis. (a) Forranis, Fret, n= m xax = d²x The qXG qE m at? Id² = go dt m For z anis: Force acting in zaris -0.

(ط) any time to n amis Along ang 21 spaling motion motion. a(y) = 4ox (t) + L ant2 alt=0+ [ al a(t) = QE+2 Along + tax + am (z anis az =0. At ang time (&)., z(t) = Voxt z(t) = Vot anis Along 19) Neither the force velocity is along gani asis. Therefore, nor the initial There is no displacement alors olong yari