Here is an interesting problem shared by Neeraj.
Let us make the following assumptions:
1) The electric field is along the axis
2) The magnetic flux density is along the axis
3) Gravity is along the axis
Let the particle\s initial velocity be , and let its charge be and its mass be .
Computing the forces on the particle results in:
The first equation yields:
So the velocity in the direction is initially negative. When the gravity becomes the only force remaining, it acts in the direction. So the speed of the particle diminishes as the velocity becomes less negative, before increasing again as the velocity becomes positive. The minimum speed in the direction is zero, and it reaches this value at: