Charged particle at rest in magnetic field with oscillating electric field

[BishwasG]

I can't figure out what is the motion of a charged particle at rest at origin in a constant uniform magnetic field when it is subjected to an oscillating electric field starting t = 0. I need to find the equations representing its motion.

 

[AuraCrystal]

Use the Lorentz force law$\mathbf{F}=q(\mathbf{E}+\mathbf{v} \times \mathbf{B})$ where F is the force, q is the charge, E is the electric field and B is the magnetic field. Then, you substitute the resulting expression into Newton's Second Law, $\mathbf{F}=m\mathbf{a}$. Then you just plug and chug and solve the resulting Diff. Eq. (You didn't specify the directions of the E and B fields, so I can't go any further. xP)

Hope that helps!

 

[BishwasG]

E and B fields are perpendicular. I have to take into account the damping and resisting forces for the oscillatory motion. I need to find a solution analytically for the motion of the particle in that case. I managed to do it, but I am not sure if I did it right. If the B field is along y-axis and E along x, I found an oscillatory motion in xz plane. The damping factor brings it to rest as time goes to infinity.

 

[jfy4]

You should post the full details of the problem.