
Magnetic
Field Vectors and Components 

The
magnetic field at any point in space is a vector quantity.
This means there is a direction associated with the field
as well as a field strength. Consider the arrow below:


The
direction of the arrow can be thought of as the direction
of the magnetic field. The length of the arrow can be
thought of as the strength of the field, i.e. the longer
the arrow, the stronger the field. Call this length B.

If I place set of axes on the arrow I can divide the field
into two components of the field, namely the x component
and the y component. Call these lengths Bx and By. 

I
can now describe the length of the arrow, or the strength
of the magnetic field, in terms of the x and y components.
Using the Pythagorean Theorem: 

Now
imagine that there exists a third direction, so that the
arrow, B can be pointing out of (or into) the plane of
the page. There is now a third compnent, namely Bz, which
in our example is the length of the component stretching
from the page outward to the tip of the arrow. 

By
exactly the same mathematics, I can now describe B as:


The value B, is the strength of the magnetic field.
Bx, By, and Bz are the three components measured by
a three axis teslameter (gaussmeter). A single axis measuring device
will change its reading depending on which way the sensitive
axis is oriented with respect to the direction of the
magnetic field. To obtain a complete representation
of magnetic field at any point in space, one needs not
only the value of B, but the direction, which can be
expressed as the three components, Bx, By and Bz.
Some magnetic field sensors measure only one component
of the magnetic field (Fluxgates and Hall effect instruments).
These are referred to as single axis devices.
Other instruments measure only the total field amplitude
(NMR, ESR). This is the quantity B above.
It is possible to combine three axis sensors to give
three field measurements in a single probe package.
These are referred to as threeaxis devices.
Brian Richter, August, 1999



