Q. 514.0( 2 Votes )

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.

Answer :

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.


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