Charged Particle in a Uniform Electric Field

now that we've established that you can

make a uniform electric field we've

charged parallel plates a logical next

step would be to see how a charged

particle moves in such a few just as

before is instructive to look at a

parallel case in gravitation where we

have and where have we encountered

parallel gravitational fields near the

surface of the earth the gravitational

field is of the same strength G and

pointing down we know that the standard

equations are kinematics apply to this

case because there is a constant

downward acceleration similarly in a

uniform electric field a charged

particle experiences a constant force no

matter where is equals the QE and thus

constant acceleration equals to QE over


thus we can solve for the motion of a

charged particle with any initial

velocity by splitting the velocity in

the direction of the electric field and

perpendicular to it perpendicular to the

electric field the velocity of the

particles unchanged because there's no

force acting in the direction and

therefore the motion of the particle in

that direction is simply s equals to V T

the velocity parallel to the

acceleration follows the kinematics

equation v equals to V naught plus eg

and the motion is s equals to V naught T

plus half ay T squared which you should

know to be the standard kinematics

equations taking it all together the

charged particle will move in a parabola

just as we've seen in projectile motion