Electrons all have the same charge (

), and the same
mass (

).
Today we will measure the
ratio of
these two values, (

) by observing electrons as
they travel through
a gas that illuminates their trajectory.
Lorentz Force
We're going to shoot electrons with a controlled velocity (
v)
into a region with a uniform magnetic
field (
B)as shown
below.
The X's indicates the vector quantity is going away from
you.
The dots indicate that the vector quantity is going towards you.
When a charged object with charge (
q) moves through
a magnetic field (
B),
at a velocity (
v),
it experiences a magnetic force (
F) given by the vector
equation,

.
(The boldfaces type of the F, v and B
indicate that these quantities have a vector character, that is..they
have a specific direction, sometimes, textbooks write vectors with
boldface type, so the same vector equation can be written as....F=q v X B.)
This equation governs the way that charged objects behave in a magnetic
field.
- the faster the charge moves (v), the greater
the force
(F).
- the greater the magnitude (B), the greater
the force (F).
- q can
be either positive or
negative. For electrons, q is negative.
- The funny-looking cross means that the force is.......perpendicular to both the velocity
AND the magnetic field.
This last item, means that a charged object moving perpendicular to a
constant magnetic field, will go around in a circle,
like
this.
and
this.
In this lab, we will shoot electrons into a uniform magnetic field and
observe this circle.
Helmholtz Coils
Making the uniform magnetic field requires a pair coiled wires called
Helholtz coils.
It isn't hard to make a magnetic field, all you need is to run a
current down a wire. The field goes around the wire as seen in
this demonstration.
By placing two coils parallel to eachother, we can create a regtion of
magnetic field between them, where the field is uniform.
Try to do this with this little
demonstration.