XVII
281
FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS
=
=
and call p, q, r the components of the magnetic current.
Further we put P, P, Q, 7, R₁ = 7 and call P, Q, R₁ the
components of the vector-potential of this current.
electric forces produced by the magnetic current are
Then the
X₁ = A
-
dy Əz
Y₁ = A ǝz
ӘР,
ƏR,
მე
ᎧᏢ, . ᎧQ, ᎧᎡ,
+ +
дх dy Əz
= 0
(3).
aq,
ap,
Z₁ = A
Jx
-
ду
The reasoning which allows us to infer from the forces (1)
that the mutual potential of two electric current-systems
u, v₁, w₁ and u2, V2, w₂ has the form
Α
Aff
(u₁u₂+v₁V₂+w₁₂)dт₁dт₂,
leads to the conclusion, using forces (3), that the magnetic
current-systems P1, 1, 71 and P2, 12, 72 have the mutual
91,
potential
A' f f = (P₂P₁ + 919
A2 (P1P2 +9192 +™₁r₂)dt₁dt½ ·
The same considerations which led us from that potential
of electric currents to the inductive forces (2) allow us from
the potential of magnetic currents to infer the existence of
induced magnetic forces of the form
L₁ =
= -
A² dP,
dt
M₁ =
=
-
A2
dQi
dt
N₁ =
-
A2 dR₁
dt
(4).
Here also we may affirm that these forces act inside the
magnetic bodies as well as in the space outside; and we
easily convince ourselves that we cannot well confine the
connection between the force (3) and (4) to the case where
the forces (3) are due to magnetic currents alone. We must
conclude that when a system of currents or magnets gives rise
to electrical forces of the form (3), then a variation of this
system will give rise to magnetic forces of the form (4).