Chapter 2 Review of Forces and Moments - Brown University

Electrostatic forces acting on two small charged objects that are a large distance apart
Coulomb’s Law states that if like charges Q
1
and Q
2
are induced on two particles that are a distance d
apart, then particle 1 will experience a force
QQ
1 2
F=−
e
2 12
4πε d
(acting away from particle 2), where ε is a
fundamental physical constant known as the
Permittivity of the medium surrounding the particles
(like the Gravitational constant, its value must be
determined by experiment).
F
+Q 1
e 12
d
+Q 2
In SI units, Q1,
Q
2
are specified in Coulombs, d is in meters, and ε is the permittivity of free space, with
2 -1 -3
fundamental units Amperes kg m . Permittivity is more usually specified using derived units, in
Farads per meter. The Farad is the unit of capacitance.
The value of ε for air is very close to that of a vacuum. The permittivity of a vacuum is denoted by ε
0
.
-12 -1
In SI units its value is approximately 8.854185 × 10 Fm
Like gravitational forces, the electrostatic forces acting on 3D objects with a general distribution of
charge must be determined using complicated calculations. It’s worth giving results for two cases that
arise frequently in engineering designs:
Forces acting between charged flat parallel plates
F
Two parallel plates, which have equal and opposite charges Q and
are separated by a distance d , experience an attractive force with
magnitude
F = Q 2 /(2 ε )
The force can be thought of as acting at the center of gravity of the
plates.
+Q
Q
F
d
Two parallel plates, which have area A, are separated by a distance d, and are connected to a powersupply
that imposes an electrical potential difference V
across the plates, experience an attractive force with
F
magnitude
2 2
+V Area A
F = AV ε /(2 d )
+
d
The force can be thought of as acting at the center of
V
- V
gravity of the plates.
Area A
F