Accelerating Charge Through
A Potential Difference
Difference in potential
(potential difference ∆V)
Directly from the
definition of potential
-
+
(V=W/Q)
The potential energy
given to a charged
particle by an electric
field is given by
W = ∆ VQ
where
Distance
d
∆V is the potential
difference that the
charge falls through
This potential energy is converted totally
to kinetic energy by the time the charge
strikes the oppositely charged plate
Difference in potential
(potential difference ∆V)
-
+
Distance
d
Notice that energy
given to the charged
particle has no
dependence at all on
the distance d
between the plates. It
is only dependent on
the charge of the
particle and the
potential difference
between the plates
1. Calculate the final kinetic energy of 1) an electron 2) a proton
accelerated in opposite directions through a p.d. of 5kV .
2. Calculate the maximum velocity of each.
-
+
Because W=VQ the
potential energy that they
have due to the field is
the same before the start
of their journey.
5 000 V
This becomes kinetic
energy as they are about
to strike the opposite
plate.
How can we calculate the final velocity of each of them?
Difference in potential
(potential difference ∆V)
+
F
The force on the
charged particle is
constant within the
field.
F=QE
Force
on the
particle
Acceleration
of particle
(because the field is
uniform E i.e. it has the
same value at each
point)
Also As F=ma
(And the mass of the
particle remains the
same the acceleration
of the particle is also
constant
Distance within field r
Distance within field r
A charged electron which enters a uniform electric field at right angles
to it accelerates at right angles to the field. There is no component of
this acceleration in the horizontal direction
-
+
Horizontal motion (constant velocity)
The resulting path of
the electron is
parabolic
Constant
Acceleration due to
the field