Before we
start to talk about how the
Gaussian gun works, first we have to understand how kinetic and
potential
energy work. The easiest way to demonstrate this is to start with a
pendulum swing. As the ball moves from the top of one end to the other,
it moves
faster
as it reaches the bottom point and then the speed of the ball starts to
decrease. We can use this as an example of potential and kinetic
energy. When
the ball is at the highest point it only has potential energy due to
gravity
and height. But as the ball moves down along the trajectory line,
it  starts to
lose potential energy and gain kinetic energy. Inside the gravity
field, the
potential energy of the object is simply calculated as its weight times
its
height. The simple motion of satellites in orbit can also be explained
as a
periodic exchange of potential and kinetic energy. As all of us know
that
potential and kinetic energy must sum up to zero and that is
conservation of 
energy. 
       
I used the
pendulum
as an introduction because it illustrates the relationship between
potential
and kinetic energy via gravitational force. We can think of magnetic
force as
the gravitational force. When we place the metal ball close to the
magnets, the
magnetic force from the magnets starts to pull the ball in. I will use
figure 3
as my demonstration of how magnetic force works. When you try to pull
the metal
ball away from the magnets, the magnetic force becomes weaker. Just
like the
force of gravity, when we get further away from the center of the earth
the
force of gravity becomes weaker. By weaker I mean the force that acts
on the
object decreases.
        The
magnetic force
requires us to do work to pull the metal ball and magnets apart.
Remember one
thing, that the work is defined as force times distance. When the ball
is closer
to the magnets, the pulling force is very strong. Indeed, it’s
difficult to
hold the ball close, but separate from the magnet. As the distance
between the
ball and the magnets increases, the force weakens considerably.
Source: http://seniorphysics.com/physics/gaussian_gun.jpg