MOTION MOUNTAIN

liquid electricity, invisible fields and maximum speed 45
to describe the magnetic field by the quantity*
0 −B z B y
B=( B z 0 −B x ) , (9)
−B y B x 0
called anantisymmetric tensor.
The magnetic field is defined by the acceleration it imparts on moving charges. This
acceleration is observed to follow
a= q v×B (10)
m
Challenge 22 s
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Vol. II, page 38
Vol. I, page 110
for a chargeqwith massm.The relation is often calledLorentzacceleration, after theimportant
physicist Hendrik A. Lorentz** who first stated it clearly.*** The Lorentz acceleration,alsocalled
theLaplace acceleration,definesthemagnitudeandthedirectionof
the magnetic fieldB. The unit of the magnetic field is called tesla and is abbreviated T.
We have1 T=1 N s/C m=1 V s/m 2 =1 V s 2 /A m.
The magnetic field is defined and measured by its influence moving charges. Let us
explore the definition. Does the definition of magnetic field given here assume a charge
speed much lower than that of light?
The definition of the magnetic field assumes, like that of the electric field, that the test
chargeqis so small that it does not disturb the fieldBto be measured. Again, we ignore
this issue, which means that we ignore all quantum effects, until later in our adventure.
The definition of the magnetic field also assumes thatspace-timeisflat,anditignores
all issuesdue tospace-timecurvature.
The Lorentz acceleration is the fundamental effect that a magnetic field has on a moving
charge. The Lorentz acceleration is the effect at the root of any electric motor. An
electric motor is a device that uses a magnetic field as efficiently as possible to accelerate
charges flowing in a wire. Through the motion of the charges, the wire is then also
* The quantityBwas not called the ‘magnetic field’ until recently. We follow here the modern, logical
definition,whichsupersedesthetraditionalone,whereBwascalledthe‘magneticfluxdensity’or‘magnetic
induction’andanotherquantity,H,wascalled–incorrectly,butforoveracentury–themagneticfield.This
quantityHwill notappear inthiswalk, but itisimportant forthedescription ofmagnetismin materials.
** For more details about Hendrik A. Lorentz (b. 1853 Arnhem, d. 1928Haarlem), see the volume on relativity.
*** The expressionv×Bis the vector product of the two vectors. The most practical way to calculate the
vectorproductv×Bcomponent bycomponent isgiven bythedeterminant
e x v x B x
v×B= e y v y B y
e z v z B z
+ − +
or,more sloppily v×B= v x v y v z . (11)
B x B y B z
Thisiseasytorememberandeasytoperform, both with lettersandwith numerical values.(Here,e x isthe
unitbasisvector inthexdirection.) Written out, itisequivalenttotherelation
whichisharder toremember.
v×B=(v y B z −B y v z ,B x v z −v x B z ,v x B y −B x v y ) (12)
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net