Uniform Electric Field between
Parallel Charged Plates
Constant force on a charged
particle

Example
Determine the force on a proton
between two parallel plates.
(E=6 x 104 N/C, m=1.67x 10-27kg)
Electric Potential Energy



Potential of Electrostatic Force to Do
Work
Relate to Work done by External
Force in Moving Charge
Expressed in Terms of Electric
Potential Difference
Electric Potential and Potential Energy
E
F = qE
+q
d
Work is done on the charge!
(Potential) Energy of the objected increased by
W = Fd = qEd = q V
E
E
F = qE
+q
d
F
Electric Potential Difference
V= E-field x distance
[V] = N.m/C
= J/C
= Volt
V
Potential increases as moving
against E-field.
Work done to unit charge.
0
d
E
-q
F = qE
+q
d
Low potential
A
High potential
B
Potential energy for +q increases A -> B.
However, potential energy for –q increases B -> A.
Electric potential at B is higher than at A for both..
Energy and Charge Movements


A positive charge gains electrical potential
energy when it is moved in a direction
opposite the electric field
If a charge is released in the electric field,
it experiences a force and accelerates,
gaining kinetic energy
• As it gains kinetic energy, it loses an equal
amount of electrical potential energy

A negative charge loses electrical potential
energy when it moves in the direction
opposite the electric field
Energy and Charge
Movements, cont



When the electric field
is directed downward,
point B is at a lower
potential than point A
A positive charge that
moves from A to B
loses electric potential
energy
It will gain the same
amount of kinetic
energy as it loses
potential energy
Summary of Positive Charge
Movements and Energy

When a positive charge is placed in
an electric field
• It moves in the direction of the field
• It moves from a point of higher
potential to a point of lower potential
• Its electrical potential energy decreases
• Its kinetic energy increases
Summary of Negative Charge
Movements and Energy

When a negative charge is placed in
an electric field
• It moves opposite to the direction of the
field
• It moves from a point of lower potential
to a point of higher potential
• Its electrical potential energy decreases
• Its kinetic energy increases
E
a
d
a
+q
How much of work has been done on the charge?
W = qE dcos(a)
Electric potential changed by V = E d cos(a).
Important!!
Motion perpendicular to E-field does not change potential.
Equipotential Line
v
v
v
v
+ +
+
+
+
+
+
+
+
+ +
+
Surface of conductor
ll
Equipotential surface
Equipotential Surfaces

An equipotential surface is a surface
on which all points are at the same
potential
• No work is required to move a charge at
a constant speed on an equipotential
surface
• The electric field at every point on an
equipotential surface is perpendicular to
the surface
Two parallel conducting plates are charged as shown
in the figure. An electron is injected between the
plates from the left side (see figure). Which curve
describes the trajectory of the electron correctly?
+
-
v
1.
2.
3.
4.
-
A
B
C
D
+
A
-
+
-
+
-
+
-
+
-
+
-
+
-
-
B
C
D
Comparison with GRAVITY
Gravitational
(on the earth)
Electric
Mass, m (Kg)
Only 1 type
g (m/s2=N/Kg)
Charge, Q (C)
+ and E-field (N/C)
mgh (Nm = J)
QEd (J)
Potential enery
Potential energy
gh (Nm/Kg)
Ed (Nm/C)
Gravitational potential
Electric potential
Prob. 27
E = 3500 N/C
Q
*
70 cm = 0.7 m
1.Is Q positive or negative?
2.How large force would a +1 C charge experience at *?
3.What is Q value?
A2. Electric field: force on a positive unit charge FE = qE.
FE = (+1 C)(3500 N/C) = 3500 N
A3. FE = qE = k|Q|.|q|/r2
3500 N = (8.99x109 Nm2/C2) (Q C)(+1 C)/(0.7 m)2
Q = -1.9x10-7 (C) negatively charged
-Q
- - -
-
-
-
-
-
V=e
-
e
+Q
Q
Q=C
e
e
Capacitanc
e
The Electron Volt

The electron volt (eV) is defined as the
energy that an electron (or proton)
gains when accelerated through a
potential difference of 1 V
• Electrons in normal atoms have energies of
10’s of eV
• Excited electrons have energies of 1000’s of
eV
• High energy gamma rays have energies of
millions of eV

1 eV = 1.6 x 10-19 J
Example



Car battery (12V)
Work done to move a proton from A
to B
Work done to move an electron from
A to B