# Motion of Charged Particle Through Electric Field

♦ Study about the Motion of Charged Particle Through Electric Field . The path of the particle in the Electric  field is parabolic  ♦

Consider a particle of mass m , charge q , moving horizontally with velocity u , as shown in the figure. The charge enters a region between two parallel plates (length L), where an electric field E , as shown exists. Since, there is no horizontal force on the particle , the horizontal component of velocity does not change ,
vx = u at all times . The time spent by the particle in the field region is

t = L/u

During this time, the particle experiences a vertical force Fy = qE . Due to this force acceleration in
Y-direction is ay = qE/m . In time t , the velocity acquired in Y-direction is

vy = ayt

vy = qEL/mu

The angle θ , at which the particle emerges out of the field (figure) is

tan θ = vy/vx

The velocity with which the particle comes out of the field is

The path of the particle in this case is parabolic this can be seen as follows. In any time t, the distances traveled by the particle in x, and y direction are

eliminating t , we get

y ∝ x2

The path is a parabola.