A particle having mass m and charge q is release from the origin in a region in which electric field and magnetic field are given by

Find the speed of the particle as a function of its z-coordinate.

Given-

Mass of the particle = m

Charge of the particle = q

Electric field and magnetic field are given by

Velocity,

Magnetic force, we know, Lorentz force F is given by -

where,

q = charge on an electron

v = velocity of the electron

B=magnetic field

θ= angle between B and v

Also, coulomb’s force experienced by the electron is given by,

where e= charge on the electron and

E= electric field applied

So, total force on the particle,

=q

= q

Now, since

,

So, acceleration is given by

From 3^rd equation for motion

where

u = initial velocity

v= final velocity

s=distance travelled

and a = acceleration of the particle

So,

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