MOTION MOUNTAIN

liquid electricity, invisible fields and maximum speed 53
Challenge 31 e
moving with the rods would see an electrostatic repulsion between the rods given by
ma e =− 1 2λ 2
4πε 0 d
(21)
Challenge 32 e
whereλis the charge per length of the rods. A second,resting observer sees two effects:
the electrostatic repulsion and the attraction discovered by Ampère.The second observer
therefore observes
ma em =− 1 2λ 2
4πε 0 d +μ 0λ 2 v 2
2π d . (22)
Challenge 33 d
Page 232
Challenge 34 d
This expression must be consistent with the observation of the first observer.This is the
case only if both observers find repulsions. It is easy to check that the second observer
sees a repulsion, as does the first one, only if
v 2 < 1
ε 0 μ 0
=c 2 . (23)
This maximum speedc, with a value of0.3 GM/s, is thus valid for any object carrying
charges. But all everyday objects contain charges: there is thus a maximum speed for
matter.
Are you able to extend the argument for a maximum speed to neutral particles as
well? We will find out more on this limit velocity, which we know already, in a minute.
Another argument for magnetism as a relativistic effect is the following. In a wire with
electrical current, the charge is zero for an observer at rest with respect to the wire: the
wire isneutral for that observer.The reason is that the charges enter and exit the wire at
the same time for that observer. Now imagine an observer who flies along the wire.The
entrance and exit events do not occur simultaneously any more; the wire ischarged for a
moving observer. (The charge depends on the direction of the observer’s motion.) Now
imagine that the moving observer is electrically charged. He will be attracted or repelled
by the wire, because for him, the wire is charged. The moving observer will say that the
attraction is due to the electric field of the wire. The observer at rest will also note the
attraction or repulsion of the moving observer, but since for him, the wire is neutral, he
will deduce that moving charges experience a force – possibly with a slightly different
value, but this is a technicality – due to the electric current in the wire; the observer at
rest will thus say that a wire with a current is surrounded by amagnetic field which only
produces an effect on charges that move.
In summary, electric effects are due to more or less static electric charges and to their
electric fields; magnetism, magnetic effects and magnetic fields are due tomoving electric
charges.*The existence of magnetic fields is a relativistic consequence of the existence of
electric fields. In particular, magnetism is not due to particles with magnetic charges.
Such particles, called magnetic monopoles, do not exist. (Magnetic charges can be intro-
* ‘Electrons move in metal with a speed of about1µm/s; thus if I walk with the same speed along a cable
carrying a constant current, I should not be able to sense any magnetic field.’ What is wrong with this
argument?
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net