Transcript Motion of Charged Particles in a Uniform Electric Field

Motion of Charged Particles
in a Uniform Electric Field
Montwood High School
AP Physics C
R. Casao
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
a
we can apply the two-dimensional
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:
v yf
tan θ 
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.