Describe the motion of a charged particle in a combined electric and magnetic field.

Explanation

Let E be the uniform electric field applied in the y direction and B be the uniform magnetic filed applied along the z direction.
Let the change q move with a speed v along the x direction.
i.e., `vec(E)=Ehat(j), vec(B)=Bvec(k) " and " vec(v)=vhat(i)`
`therefore " "vec(F)_(e)=qEvec(j)` (electric force)
magnetic force `" "vec(F)_(mag)=qvec(v) times B=qvhat(i) times Bhat(k)`
i.e.,`" "vec(F)_(m)=qvB(-vec(j))`
By applying Fleming's Left Hand Rule, we note that the resultant force on the charged particle
`" "vec(F)=qEhat(j)-qvBhat(j)`
i.e.,`" "vec(F)=q(E-vB)hat(j)`
If qE = qvB, then net force on the change will be zero and the charge continues to move along x direction without deflection.
Since qE = qvB, `v=E/B` where 'v' is called the velocity. E and B are called crossed fields.
The crossed fields `vec(E) " and " vec(B)` may be used to select charged particles of a particular velocity out of a beam containing charges moving with different speeds.