When a small test charge q travels with velocity uv in a magnetic field characterized by a
magnetic flux density B
v
(Wb/m2), it will experience a magnetic force F qu B m
v v v
= × . If there
is an electric field E
v
as well, the total electromagnetic force is governed by the Lorentz’s
force equation:
F q(E u B)
v v v v
= + × (11.1)
Historically, B
v
is defined by measuring m F
v
and uv experimentally. However, we will start
with two fundamental postulates of magnetostatics in free space to define B
v
, from which all
experimental laws and the concept of magnetic “potential” can be derived.