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Robert G. Brown rgb at phy.duke.edu
Tue Oct 22 09:29:31 PDT 2002

On Tue, 22 Oct 2002, Karen Shaeffer wrote:

> On Tue, Oct 22, 2002 at 02:15:08AM -0400, Ken Chase wrote:
> >
> > [A friend told me about blowing a circuit once at his lab and he had a large
> >  metal bracelet on. When the circuit blew, he was standing under the power
> >  run (about 5 feet over his head in the ceiling) and his bracelet shot up his
> >  arm and yanked on his wrist, quite hard! He had a bruise to prove it.  It
> >  was only a 20A circuit - what would cause that? Dangerous wiring situation?]
>
>
> That would be Faraday's Law. Look it up in any College Physics Book. The
> bracelet was a closed circuit that was enclosing Magnetic flux from the
> power line. Basically, the rate of change of the magnetic flux enclosed
> within the cross-sectional area bounded by the closed circuit resulted
> in a force on the bracelet. Since the cirucit breaker broke, this
> resulted in a large rate of change and a proportional force.

Well, yeah, but the magnetic field is so damn weak, and ordinarily the
cables would carry balanced currents inside a shielding grounded
conduit...

Just for fun (feel free to correct any of this, anybody, as although I
teach all this physics, there is a bunch of estimation below and my
arithmetic skills are terrible:-):

2 meters away, the magnetic field of a completely unshielded long
straight line carrying 20 amps of current should have been order of a
microtesla:

B(r) = 2 k_m I/r = 2 x 10^{-7} x 20/2(meters) = 2 x 10^-6 Tesla

The mutual inductance of the bracelet, assuming it to be order of 5 cm
in radius and neglecting variation of the field across it is something
like

\phi_m = B(I)*A = (2 k_m I / r) * \pi R^2 = 10^-7 I \pi (.0025)

or (estimating \pi \approx 4 and dividing by I in the wire):

M \approx 10^-9 Henries.

The induced voltage is

V_bracelet \approx M dI/dt

which alas is not very knowable without knowing dI/dt.  If the line
current dropped to zero VERY quickly this could be quite large, but
usually a similar induced voltage causes e.g. arcing that keeps it from
being that large.  If we assume that the current drop occurs in a
microsecond, V_b could be order 0.1 volts.  Assuming that the resistance
of the bracelet is very small, even this voltage could create a single
pulse of current.  Making it a very generous I_b = 1000 amps (assuming
that the resistance of the bracelet is around 0.001 ohms) the peak force
of attraction should have been strictly less than (and WAY less than,
since forces on the half of the bracelet nearest the wire should have
been nearly cancelled by forces on the far half of the bracelet)
B(r)*I*(0.1) or less than 0.0001 Newton's (lasting a tiny fraction of a
second) which should hardly have made his hand jump up.  Even if there
were a single unshielded power bus carrying several hundred amps PLUS
the inductive current peak order a kiloamp, the two meters and extremely
short duration of the attractive force should have imparted almost no
momentum to the bracelet.

Among our demos, we have a "magnetic cannon" which consists of a coil
with maybe a thousand turns wrapped around an iron core (which confines
and significantly enhances the resulting magnetic field).  A conducting
ring some 3 cm across is placed over the iron core and electric line
current is switched on with an ordinary switch, where I'm guessing that
the line current is order of 1 A peak.  The ring jumps off quite
satisfactorily.  However, it doesn't shoot as high as the ceiling (it
goes up maybe half a meter) and can easily be held down with a hand,
although it gets very hot very quickly if one does this as it acts like
a transformer coil.

So I'm just surprised that a single line, with field unenhanced by iron,
could create so great an impulse in a similar conducting ring roughly
two meters away.  I'd love to understand how it happened.

rgb

Robert G. Brown	                       http://www.phy.duke.edu/~rgb/
Duke University Dept. of Physics, Box 90305
Durham, N.C. 27708-0305
Phone: 1-919-660-2567  Fax: 919-660-2525     email:rgb at phy.duke.edu