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[moderator note: Thread title changed to make it descriptivie of the problem]

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

B= -B' j and E= E' k

where j and k are unit vectors along y axis and z axis respectively.

Find the speed of the particle as a function of z co ordinate.

The particle is released at the origin so at t=0 only electric force will act on the particle along z axis. As the particle gains some velocity, magnetic force will start acting and will push the particle in xz plane. Here the velocity has two components, x and z, so magnetic force will act on both these components. I calculted the net force in both x and z directions as:

F

F

As can be seen from the equations, the acc. in the both the directions is variable , so how come in the solution(picture), he has used the equation v

## Homework Statement

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

B= -B' j and E= E' k

where j and k are unit vectors along y axis and z axis respectively.

Find the speed of the particle as a function of z co ordinate.

**2. Relevant questions:**

## The Attempt at a Solution

The particle is released at the origin so at t=0 only electric force will act on the particle along z axis. As the particle gains some velocity, magnetic force will start acting and will push the particle in xz plane. Here the velocity has two components, x and z, so magnetic force will act on both these components. I calculted the net force in both x and z directions as:

F

_{x}= qBv_{z}F

_{z}= q(E-Bv_{x})As can be seen from the equations, the acc. in the both the directions is variable , so how come in the solution(picture), he has used the equation v

^{2}- u^{2}= 2as?