ACCELERATION IN UNIFORM ELECTRIC
FIELD
 The
motion of a charged particle in a
uniform electric field is equivalent to
that of a projectile moving in a uniform
gravitational field.
 When a charge q is placed in an electric
field E, the electric force on the charge is
F = E·q.
 From Newton’s second law, F = m·a,
therefore, m·a = E·q.
Eq
 The acceleration of the charge is: a 
m
ACCELERATION IN UNIFORM ELECTRIC
FIELD

If E is uniform (constant in
magnitude and direction),
then the acceleration is
constant.
 If the charge is positive,
the acceleration will be in
the direction of the
electric field.
 If the charge is negative,
the acceleration will be in
the direction opposite the
electric field.
ACCELERATION IN UNIFORM ELECTRIC
FIELD
The electric field in the region
between two oppositely charged
flat metal plates is considered to
be uniform.
 If an electron is projected
horizontally into an electric field
with an initial velocity vo, it will
be accelerated by the electric
field.

ACCELERATION IN UNIFORM ELECTRIC
FIELD
The acceleration will be in the positive y direction (the
direction of the electric field).
 Because the acceleration is constant,
Eq
we can apply the two-dimensional
a
m
kinematics equations for
projectile motion:
vo = vx = constant
(no acceleration in the
horizontal direction)

ACCELERATION IN UNIFORM ELECTRIC
FIELD
 Final
vertical speed: vyf = vyi + (a·t); initial
velocity in y-direction is zero because the electron
enters the field horizontally.
 Vertical displacement:
Dy = (vyi·t) + (0.5·a·t2)
 Horizontal displacement: x = vx·t
 The time t that the electron is accelerating
vertically within the electric field is equal to the
time during which it is traveling horizontally
through the electric field.
ACCELERATION IN UNIFORM ELECTRIC
FIELD
Once the electron leaves the uniform electric
field, it continues to move in a straight line with
a speed greater than its original speed.
 The angle at which the electron exits the electric
field is given by:

tan θ 
v yf
vx
Forces on electron beam in a TV tube (CRT)
F = Q E and F = m g (vector equations)
TV tube with electron-deflecting charged
plates (orange)
F=QE
WHAT ABOUT GRAVITY?
 The
gravitational force acting on the mass
of the electron has been neglected because
the magnitude of this force is 9.11 x 10-31
kg ·9.8 m/s2 = 8.9278 x 10-30 N, which is
small in comparison to the electric force
acting on the electron.
 The same is true for a proton.