Question

A particle of mass m and charge q is released from the origin in a region in which the electric field and magnetic field are given by
`vecB = -B_0 vecj and vecE = E_0 vecK `
Find the speed of the particle as a function of its z-coordinate.

Answer 1

Given:
Mass of the particle = m
Charge of the particle = q
Electric field and magnetic field are given by
`vecB = -B_0 vecj and vecE = E_0 vecK`
Velocity, `v = v_xhati + vyhatj + v_zhatk`
So, total force on the particle,
F = q (E + v × B)
`= q [E_0hatk - (v_xhati + vyhatj + vzBoi)`
`= v_x = 0,`
so, `a_z =(qE_0)/m`
`v^2 = u^2 + 2as = 2(qe_0)/m z`

Here, z is the distance along the z-direction.