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 3rd 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.