The short answer to your question is yes, a current flowing through a
conductor in a magnetic field will induce a force upon the conductor
which, assuming the conductor is not fixed, will cause it to move.
Common applications of this are the electric motor and loudspeaker.
Given a constant magnetic field strength and electric current, the
force induced is proportional to the component of the current flowing
perpendicularly (at 90 degrees) to the magnetic field. In other
words, if the wire carrying the
current is running in the same direction as the magetic field then no
force will be induced. Equally, if the wire is completely
perpendicular to the direction of magnetic field, then the force will
be at a maximum value.
A simple diagram of this is available in section 2 of:
As stated by the site above, the size of the force induced in Newtons,
F = Bil sin(theta)
where B is the magnetic flux density (in Webers), i is the current
flowing through the wire (in amps), l is the length of the wire in the
field (in metres), and theta is the angle of the wire witrh respect to
the direction of the magnetic field.
The direction of movement of the conductor can be determined throught
the use of Fleming's Left Hand Rule. By positioning one's left hand
as shown in the diagram in the Audio Systems page
with the first finger pointing in the direction of the magnetic field
and the second finger in the direction of current flow (conventionally
positive to negative), the thumb will point in the direction of
movement of the conductor.
A simple explanation of why the conductor moves is available from
GCSE Bitesize: Physics
If you would like a more complex and in depth discussion of the
physics involved this article may be of interest:
Motors and Generators
Electric Motor: The Motor Effect
Science Snacks: Motor Effect
I hope this answers your question fully; if you would like any further
clarification please ask before rating my
induced current physics
fleming left hand rule
how "electric motor" works
how loudspeaker works