


Electric Force
There is a certain force associated with electric charge,
so when a net charge is produced, a net electric force is also produced.
We find electric force at work in anything that runs on batteries
or uses a plug, but that isn’t all. Almost all the forces we examine in
this book come from electric charges. When two objects “touch” one
another—be it in a car crash or a handshake—the atoms of the two
objects never actually come into contact. Rather, the atoms in the two
objects repel each other by means of an electric force.
Coulomb’s Law
Electric force is analogous to gravitational force: the
attraction or repulsion between two particles is directly proportional
to the charge of the two particles and inversely proportional to
the square of the distance between them. This relation is expressed
mathematically as Coulomb’s Law:
In this equation, and are the charges of the two particles, r is
the distance between them, and k is
a constant of proportionality. In a vacuum, this constant is Coulumb’s
constant, , which is approximately N · m^{2 }/ C^{2}.
Coulomb’s constant is often expressed in terms of a more fundamental
constant—the permittivity of free space, , which has a value of C^{2}/ N · m^{2}:
If they come up on SAT II Physics, the values for and will be given to you,
as will any other values for k when
the electric force is acting in some other medium.
Example

According to Coulomb’s Law, the electric force between
the two particles is initially
If we double one of the charges and double the value of r,
we find:
Doubling the charge on one of the particles doubles the
electric force, but doubling the distance between the particles
divides the force by four, so in all, the electric force is half
as strong as before.
Superposition
If you’ve got the hang of vectors, then you shouldn’t
have too much trouble with the law of superposition of
electric forces. The net force acting on a charged particle is the
vector sum of all the forces acting on it. For instance, suppose
we have a number of charged particles, , , and . The net force acting on is the force exerted on it by added to the force exerted on it by . More generally, in a system of n particles:
where is the force exerted
on particle 1 by particle n and is the net force acting on particle 1.
The particle in the center of the triangle in the diagram below
has no net force acting upon it, because the forces exerted by the
three other particles cancel each other out.
Example

The net force acting on A is
the vector sum of the force of B acting
on A and the force of C acting
on A. Because they are both positive
charges, the force between A and B is
repulsive, and the force of B on A will
act to push A toward the left of the
page. C will have an attractive force
on A and will pull it toward the bottom
of the page. If we add the effects of these two forces together,
we find that the net force acting on A is
diagonally down and to the left.
