MadSci Network: Physics

Re: Is it possible to focus a magnetic field to a point?

Date: Wed Nov 1 14:56:54 2006
Posted By: michael pierce, Post-doc/Fellow, Materials Science Division, Argonne National Lab
Area of science: Physics
ID: 1157614355.Ph

It is indeed possible to "focus" magnetic fields, however maybe not
quite in the sense that you're thinking.  I'm not quite sure what level to
target my explanation, so please bear with me if I'm being a bit too verbose.

Depending upon how you start, it can quickly become a confusing subject.
 There are two important extreme cases: that of static magnetic fields
(well, largely static) and those that are dynamic.  Magnetostatics is
relatively straight forward.  Depending upon the geometry of the source,
you can increase the strength of the magnetic field in particular
places.  For instance, at the center of a coil as you've already said,
or from the corners of a magnetic body.  In these places the magnetic
field can be much stronger than in other locations.  In addition, the
magnetic fields produced by relatively ordinary magnets can in fact be very
large when you measure near enough to them.

Things always seem to get more complicated when you add time.  So to have a
magnetic field that becomes extremely strong at one point in time almost
always involves not just magnetic fields, but electric fields as well.  In
this case the source used to produce the magnetic fields will almost always
involve current.  It's possible to, briefly, run a huge amount of current
through a coil to create a very intense magnetic field for a short amount
of time.  The dimensions and geometry of how the current flows are
important, but it's not as simple as as making things smaller.  

Often the best way to produce a very high magnetic field is through a
solenoid, a long coil with many, many turns of wire.  To a reasonably good
approximation the magnetic field inside the solenoid does not depend upon
the radius of the turns nor upon how close you are to the walls.  The
magnetic field depends upon the current through the wire, and the number of
times the wire wraps around in a given length, but nothing else. This is
true enough so long as the current isn't changing.  In this way you can
create a fairly high magnetic field that is "focused" over the area inside
the coils.

There are a few problems that creep in when you begin changing the current.   
Suppose you have a solenoid coil in which you wish to run more and more
current to produce higher and higher magnetic fields.
Any change in the magnetic field (or the sudden appearance of one!) will
induce a counter-current in the coils.  This current then also creates a
magnetic field.  However, in this case the magnetic produced is in
opposition to the original magnetic field.  In effect, the induced field
attempts to cancel the change.  However, it is a transient effect.  As soon
as the original field stops changing, the induced field subsides.  But in
this way the primary field produced by the original increasing current is
damped somewhat by the induced field.  I think extends pretty well to more
complicated systems, ie the induced field is always going to act in
opposition to any change regardless of how we set up the geometry.

Now, so far we have not gone directly at what you asked, that is, could you
modulate a changing magnetic field in such a way as to focus it at a
particular point.  Sort of... 

A changing, traveling magnetic field is going to be accompanied by a
changing, traveling electric field.  So in essence this would involve
modulated EM waves, not just a magnetic fields.  You can think of having
light waves that are all traveling towards a common point from different
directions in a ring.  Further, suppose that they are all polarized to have
the magnetic fields all point along a common axis perpendicular to the
ring.  Lastly, make it such that they arrive in-phase at the central point.
 You would now have a large, alternating magnetic field about a single
point.  However, you'd also have alternating electric fields around too.
Another case would be an antenna that emits a focused burst of radiation. 
Depending upon the power, the magnetic field could be quite strong.  But
again you'll have both electric and magnetic fields.  

A wave-guide a varying dimensions might also do the trick up to a point. 
Depending upon the magnetic and electric fields present inside a cavity,
they have a relation between amplitude (strength of the magnetic field) and
the dimensions of the cavity.  However, changing the dimensions will have a
profound effect that will cause power loss of the waves, changing both the
frequencies and amplitudes.  

Another point of interest here is when you're not concerned with either
having the fields tightly focused or when the objects you want to influence
do not need huge fields(ie protons, neutrons, electrons or atoms).  In the
first case, if you just take a coil and run an alternating current through
it, you can create quite a bit of heat in metals placed at the center of
the coil.  This is quite useful when localized, selective heating is
needed.  The changing EM fields drive the electrons around inside the metal
making it quite hot.  Look up "RF heaters" or "induction heating" for more
info.  The other case is when you want to influence nucleons or electrons.
 In this case (with much less power) you can use an RF field to flip and
manipulate the spins of the particles.  Look up "Nuclear magnetic
resonance" for more information on that.  It is also possible to use EM
waves to "trap" small objects in a particular place.  In this case a laser
is focused to a small point and dielectric materials can be stuck or
manipulated.  This technique is known as a "optical trap" or "optical

Lastly, the term "a single point" is a little mis-leading.  The wavelength
of the light and the area over which you wish to have a magnetic field will
ultimately conspire against you.  Essentially the uncertainty principle
will come into play when you try to set the wavelength small enough and
have the focused point be small too.  However, in most cases you won't run
into this problem.

Anyhow, I hope that helps and wasn't too confusing.  My electrodynamics is
feeling a little rusty and it was nice to think about these things.  A good
source to learn a bit more would probably be from some electrical
engineering books on EM waves, antennas, wave guides, and such.  The
information they provide will give quantitative means to the above ideas
and provide some clarification (or potentially a correction).

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