Question

A point charge q is moving in uniform electric field (E0 in the z-direction) and uniform magnetic field (B0 field in the x-direction). (i) What is the force acting on the charge particle? Find equations of motion for the charge particle. (ii) Assume that initially the charge is placed the origin and has initial velocity (E0/2B0) in the y-direction. Determine position and velocity of the charge particle as a function of time. (iii) Find the trajectory of the particle and sketch path of the charged particle. Explain your results in terms of simple physical picture

Answer 1

a)

Force acting on the particle Fx =q E0  - qvyB0 x

Fy = qvxB0

now given uy = E0/2B0

so

Fx =q E0  - qvyB0 putting in uy = E0/2B0

we get Fx = qE0/2

ax = qE0/2m

so y= uyt

x= axt2/2

putting in the values we get

and

the trajectory is a parabola

I hope my answer helped you . If it did a few thumbs ups are appreciated

Comment your issues or doubts below so I can address them